The mean of a random variable, X, following a discrete probability distribution can be determined by using the formula E [X] = x P (X = x). Enter a probability distribution table and this calculator will find the mean, standard deviation and variance. \end{aligned}\] are shown in the R output below (ignore line numbers in [ ]s.). Therefore, you can use the inferred probabilities to calculate a value for a range, say between 179.9cm and 180.1cm. Use MathJax to format equations. Written, Taught and Coded by: Step 2: Multiply each possible outcome by the probability it occurs. Note: it doesn't matter whether we refer to \(E(X)\) or \(\mu \), but it is important to know that they both refer to the same thing. P (x) = Probability of value. A frequency distribution describes a specific sample or dataset. A discrete random variable \(X\)can take-on the values: A probability density function can be represented as an equation or as a graph. A probability distribution is a mathematical function that describes the probability of different possible values of a variable. It provides the probability density of each value of a variable, which can be greater than one. Working out the mode and median.Calculating basic probabilities. Consequently, the mode is equal to the value of \(x\) at which the probability distribution function, \(P\begin{pmatrix}X = x \end{pmatrix}\), reaches a maximum. Discrete means they can be counted. Share Cite Follow E\begin{pmatrix} X^2 \end{pmatrix} & = 3^2\times P\begin{pmatrix}X = 3 \end{pmatrix} + 4^2 \times P\begin{pmatrix}X = 3 \end{pmatrix} + 6^2 \times P\begin{pmatrix}X = 6 \end{pmatrix} + 7^2 \times P\begin{pmatrix}X = 7 \end{pmatrix} \\ A probability density function (PDF) is a mathematical function that describes a continuous probability distribution. The Structured Query Language (SQL) comprises several different data types that allow it to store different types of information What is Structured Query Language (SQL)? P\begin{pmatrix} X = x \end{pmatrix}\]. Var\begin{pmatrix} X \end{pmatrix} & = 2.25 By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Therefore, continuous probability distributions include every number in the variables range. The most probable number of events is represented by the peak of the distributionthe mode. Its the probability distribution of time between independent events. To generate a random number from the discrete uniform distribution, one can draw a random number R from the U (0, 1) distribution, calculate S = ( n . The p value is the probability of obtaining a value equal to or more extreme than the samples test statistic, assuming that the null hypothesis is true. Compute each of the following quantities. Each of these numbers corresponds to an event in the sample space \(S=\{hh,ht,th,tt\}\) of equally likely outcomes for this experiment: \[X = 0\; \text{to}\; \{tt\},\; X = 1\; \text{to}\; \{ht,th\}, \; \text{and}\; X = 2\; \text{to}\; {hh}. Every probability pi is a number between 0 and 1, and the sum of all the probabilities is equal to 1. Thanks for contributing an answer to Cross Validated! A Monte Carlo simulation is a statistical modeling method that identifies the probabilities of different outcomes by running a very large amount of simulations. \(X= 3\) is the event \(\{12,21\}\), so \(P(3)=2/36\). then, find the probability mass function for that distribution for a few values until you are sure you found the one with highest probability. Finding the mode given the probability of occurence, Mobile app infrastructure being decommissioned, The "mode" of sum of dependent random variables. & = \frac{650}{20} \\ IB Examiner. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. A frequency distribution describes a specific sample or dataset. \mu & = \sum_{x=1}^6 x.P \begin{pmatrix} X = x \end{pmatrix} \\ How to find the expected value and standard deviation, How to test hypotheses using null distributions, Frequently asked questions about probability distributions, Describes variables with two possible outcomes. What is rate of emission of heat from a body in space? Step 4 - Click on "Calculate" button to get discrete uniform distribution probabilities. (each step was rounded to 3 significant figures). In addition, there were ten hours where between five and nine people walked into the store and so on. A probability table is composed of two columns: Notice that all the probabilities are greater than zero and that they sum to one. Probability is the relative frequency over an infinite number of trials. The standard deviation, rounded to \(2\) decimal places is \(\sigma = 1.22\). Remember the mean is susceptible to outliers and the median will tend to have low probability density if the distribution is multi-modal. Although an egg can weigh very close to 2 oz., it is extremely improbable that it will weigh exactly 2 oz. Within each category, there are many types of probability distributions. \\( \\star a .0 .47 \\) b . If you flip a coin 1000 times and get 507 heads, the relative frequency, .507, is a good estimate of the probability. Probability distributions are used to describe the populations of real-life variables, like coin tosses or the weight of chicken eggs. You can define a discrete distribution in a table that lists each possible outcome and the probability of that outcome. To find a discrete probability distribution the probability mass function is required. One of the most important discrete random variables is the binomial distribution and the most important continuous random variable is the normal distribution. Step 1: Create a probability distribution for the variable, if not given to you. & = \frac{21}{6} \\ Press the "arrow down" key to scroll until you reach "stdDev (".) You can determine the probability that a value will fall within a certain interval by calculating the area under the curve within that interval. John Radford [BEng(Hons), MSc, DIC] \[\begin{aligned} \mu & = 3 \times P \begin{pmatrix} X = 3 \end{pmatrix} + 4\times \begin{pmatrix} X = 4 \end{pmatrix} + 6 \times \begin{pmatrix} X = 6 \end{pmatrix} + 7 \times \begin{pmatrix} X = 7 \end{pmatrix} \\ The number of times a value occurs in a sample is determined by its probability of occurrence. Describes data that has higher probabilities for small values than large values. Step 3 - Enter the value of x. Consequences resulting from Yitang Zhang's latest claimed results on Landau-Siegel zeros. The inverse cumulative distribution function is I(p) = INT (Np) Other key statistical properties are: Mean = (N + 1) / 2 Median = (N + 1) / 2 Mode = any x, 1 x N & = 3 \times \frac{3}{20} + 4 \times \frac{4}{20} + 6 \times \frac{6}{20} + 7 \times \frac{7}{20} \\ Since doing something an infinite number of times is impossible, relative frequency is often used as an estimate of probability. This selects the catalogue. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Probability of selection a heart card = 13/52. A cumulative distribution function is another type of function that describes a continuous probability distribution. Source: socratic.org. Step 3: Add the products from Step 2 together. \[M = \frac{x_1+x_2}{2}\] Find the probability that at least one head is observed. Well, here's the general formula for the mean of any discrete probability distribution with N . We start by calculating \(E\begin{pmatrix}X^2\end{pmatrix}\). When the migration is complete, you will access your Teams at stackoverflowteams.com, and they will no longer appear in the left sidebar on stackoverflow.com. For example, to calculate the probability that a student will have to wait 10 minutes to get their food we divide: (the number of students in the sample that waited 10 minutes) by (the total . The expected value of a discrete random variable \(X\) is the mean value (or average value) we could expect \(X\) to take if we were to repeat the experiment a large number of times. For example, it helps find the probability of an outcome and make predictions related to the stock market and the economy. What are the weather minimums in order to take off under IFR conditions? The mode of X X is the value x x, which is most likely to occur, with probability, p(x) p ( x). Why is there a fake knife on the rack at the end of Knives Out (2019)? A mode of a continuous probability distribution is a value at which the probability density function (pdf) attains its maximum value So given a specific definition of the mode you find it as you would find that particular definition of "highest value" when dealing with functions more generally, (assuming that the distribution is unimodal under . The probability density function f(x) and cumulative distribution function F(x) for this distribution are clearly f(x) = 1/N F (x) = x/N for x in the set {1, 2, , N}. Therefore, the distribution of the values, when represented on a distribution plot, would be discrete. Each probability \(P(x)\) must be between \(0\) and \(1\): \[0\leq P(x)\leq 1.\], The sum of all the possible probabilities is \(1\): \[\sum P(x)=1.\]. If you take a random sample of the distribution, you should expect the mean of the sample to be approximately equal to the expected value. The probability that a person owns zero sweaters is .05, the probability that they own one sweater is .15, and so on. If you want to cite this source, you can copy and paste the citation or click the Cite this Scribbr article button to automatically add the citation to our free Citation Generator. Each has an equal chance of winning. Theyre idealized versions of frequency distributions that aim to describe the population the sample was drawn from. A probability distribution is an idealized frequency distribution. They may be computed using the formula \(\sigma ^2=\left [ \sum x^2P(x) \right ]-\mu ^2\). . $\begingroup$ True, I didn't think more deeply about it, but it is easy to construct continuous distributions which are non-injective and that therefore have the same ambiguity problem in defining the median as discrete distributions. $\endgroup$ We start by reminding ourselves how to construct a cumulative probability distribution table and then learn how to use it to find the median value. Using Discrete Distributions This is a special case of the negative binomial distribution where the desired number of successes is 1. Consider the simple experiment of rolling a single unbiased dice once. MathJax reference. The mode is sometimes a good pick for a "typical" value to summarize a distribution. One option is to improve her estimates by weighing many more eggs. Geometric Distribution. In statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. A discrete random variable \(X\) has probability distribution table: Calculate the expected value \(E\begin{pmatrix}X\end{pmatrix}\). The probability distribution of a discrete random variable x lists the values and their probabilities, where value x1 has probability p1, value x2 has probability x2, and so on. If your aim is to find the probability of a single event, you can use the COUNTIF function to count values above, based on the event value and divide it by the total number of events. There are descriptive statistics used to explain where the expected value may end up. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. At least one head is the event \(X\geq 1\), which is the union of the mutually exclusive events \(X = 1\) and \(X = 2\). The expected value is another name for the mean of a distribution. \[P\begin{pmatrix} X = x \end{pmatrix} = \frac{x^2}{120}\] Mean (or Expected Value E ( X) ) In other words the mean value we can expect to obtain when rolling a dice is \(3.5\). \[P\begin{pmatrix} X = x \end{pmatrix} = \frac{x^2}{90}\]. The variance and standard deviation of a discrete random variable \(X\) may be interpreted as measures of the variability of the values assumed by the random variable in repeated trials of the experiment. If I calculate p(x) from p(x,y1). Let \(X\) denote the net gain to the company from the sale of one such policy. The expected value for a discrete random variable can be calculated from a sample using the mode, e.g. We find \(P\begin{pmatrix}X = 4\end{pmatrix} = 0.1\). That is, the probability of measuring an individual having a height of exactly 180cm with infinite precision is zero. The mean is \(\mu = 3.14\) (rounded to 2 decimal places). For example, a probability distribution of dice rolls doesnt include 2.5 since its not a possible outcome of dice rolls. Stack Overflow for Teams is moving to its own domain! Probability distributions belong to two broad categories: discrete probability distributions and continuous probability distributions. from https://www.scribbr.com/statistics/probability-distributions/, Probability Distribution | Formula, Types, & Examples. \[\mu = \sum x.P \begin{pmatrix} X = x \end{pmatrix}\] The following are the simple steps to find the expected value or mean for the discrete probability . Making statements based on opinion; back them up with references or personal experience. The suit of a randomly drawn playing card, Describes count data. Consider the given discrete probability distribution. and has probability distribution function: A discrete random variable \(X\) has the following cumulative probability distribution table: We need to find \(x_1\) and \(x_2\). You can find the expected value and standard deviation of a probability distribution if you have a formula, sample, or probability table of the distribution. "At least one head" is the event X 1, which is the union of the mutually exclusive events X = 1 and X = 2. Continuous probability distribution: A probability distribution in which the random variable X can take on any value (is continuous). Calculate the standard deviation of \(X\), A discrete random variable \(X\) can take-on the values: Is there any alternative way to eliminate CO2 buildup than by breathing or even an alternative to cellular respiration that don't produce CO2? . Concealing One's Identity from the Public When Purchasing a Home. The number of times a value occurs in a sample is determined by its probability of occurrence. the second time, then the PDF of $Y$ is $f(y) = (y-1)(.4)^2(.6)^{y-2},$ for Given a discrete random variable \(X\) and its cumulative distribution function \(P\begin{pmatrix} X \leq x \end{pmatrix} = F(x)\), the median of the discrete random variable \(X\) is the value \(M\) defined as: \[P\begin{pmatrix} X = x \end{pmatrix} = \frac{8x - x^2}{40}\]. A probability mass function is a function that describes a discrete probability distribution. What is the mode of the number of questions raised by the teacher it takes for the same student to be asked 2 questions? \[\begin{aligned} \(X= 2\) is the event \(\{11\}\), so \(P(2)=1/36\). What are some tips to improve this product photo? Continuing this way we obtain the following table \[\begin{array}{c|ccccccccccc} x &2 &3 &4 &5 &6 &7 &8 &9 &10 &11 &12 \\ \hline P(x) &\dfrac{1}{36} &\dfrac{2}{36} &\dfrac{3}{36} &\dfrac{4}{36} &\dfrac{5}{36} &\dfrac{6}{36} &\dfrac{5}{36} &\dfrac{4}{36} &\dfrac{3}{36} &\dfrac{2}{36} &\dfrac{1}{36} \\ \end{array} \nonumber\]This table is the probability distribution of \(X\). finding . CFI offers the Business Intelligence & Data Analyst (BIDA)certification program for those looking to take their careers to the next level. Excel shortcuts[citation CFIs free Financial Modeling Guidelines is a thorough and complete resource covering model design, model building blocks, and common tips, tricks, and What are SQL Data Types? What does PR X X mean? How to know whether a zero-inflated model is the way to go? There are several parameterizations of the negative binomial distribution. 14. The probabilities of all outcomes must sum to 1. 3- A school class of 120 students is driven in 3 buses to a symphonic . Given the discrete random variable \(X\), with probability distribution function: The sum of the probabilities is one. A test statistic summarizes the sample in a single number, which you then compare to the null distribution to calculate a p value. The probability mass function of the distribution is given by the formula: This probability mass function can also be represented as a graph: Notice that the variable can only have certain values, which are represented by closed circles. The mean of a random variable may be interpreted as the average of the values assumed by the random variable in repeated trials of the experiment. A better option is to recognize that egg size appears to follow a common probability distribution called a normal distribution. Some of which are: Discrete distributions also arise in Monte Carlo simulations. Describes events that have equal probabilities. Why bad motor mounts cause the car to shake and vibrate at idle but not when you give it gas and increase the rpms? Probability Distribution | Formula, Types, & Examples. Please give me hints on how do I proceed with this. This module provides three types of probability distributions: RealDistribution: various real-valued probability distributions. For the geometric distribution the expected value is calculated using the definition. Before we immediately jump to the conclusion that the probability that \(X\) takes an even value must be \(0.5\), note that \(X\) takes six different even values but only five different odd values. Is there a probability distribution function (PDF) that maximizes entropy for a given mode value? To calculate the standard deviation () of a probability distribution, find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root. a) Construct the probability distribution for a family of two children. Now that we know the variance, we can calculate this discrete random variable's standard deviation: A probability distribution is an idealized frequency distribution. The farmer weighs 100 random eggs and describes their frequency distribution using a histogram: She can get a rough idea of the probability of different egg sizes directly from this frequency distribution. In statistics, the binomial distribution is a discrete probability distribution that only gives two possible results in an experiment either failure or success. Now that we know the value of \(E\begin{pmatrix} X^2 \end{pmatrix} = 32.5\), we can calculate the variance: \[x = \left \{ 2, \ 3, \ 4, \ 5, \ 6 \right \}\]. We find the variance is: Why are taxiway and runway centerline lights off center? A discrete random variable X has a set of distinct possible values. The Mean, The Mode, And The Median: Here I introduced the 3 most common measures of central tendency ("the three Ms") in statistics. Legal. List of Excel Shortcuts It is computed using the formula \(\mu =\sum xP(x)\). If Y is the number of the question on which the student gets asked for the second time, then the PDF of Y is f ( y) = ( y 1) ( .4) 2 ( .6) y 2, for y = 2, 3, 4, . Find the probability that \(X\) takes an even value. For a random sample of 50 mothers, the following information was . Discrete values are countable, finite, non-negative integers, such as 1, 10, 15, etc. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. However, you will not reach an exact height for any of the measured individuals. There is an easier form of this formula we can use. The probability that a continuous variable will have any specific value is so infinitesimally small that its considered to have a probability of zero. A pair of fair dice is rolled. The variance (\(\sigma ^2\)) of a discrete random variable \(X\) is the number, \[\sigma ^2=\sum (x-\mu )^2P(x) \label{var1}\], which by algebra is equivalent to the formula, \[\sigma ^2=\left [ \sum x^2 P(x)\right ]-\mu ^2 \label{var2}\], The standard deviation, \(\sigma \), of a discrete random variable \(X\) is the square root of its variance, hence is given by the formulas, \[\sigma =\sqrt{\sum (x-\mu )^2P(x)}=\sqrt{\left [ \sum x^2 P(x)\right ]-\mu ^2} \label{std}\]. Published on \[x = \left \{ 2, \ 3, \ 4, \ 5, \ 6 \right \}\] A discrete random variable \(X\) has the following, Find \(P\begin{pmatrix}X = 4\end{pmatrix}\). & = \frac{9}{20} + \frac{16}{20} + \frac{36}{20} + \frac{49}{20} \\ \(x_2\) is the smallest value \(X\) can take such that: \(P\begin{pmatrix}X \leq x_2 \end{pmatrix} \geq 0.5\). Probability is a number between 0 and 1 that says how likely something is to occur: The higher the probability of a value, the higher its frequency in a sample. \[\begin{aligned} What are the two types of probability distributions? Discrete distribution is a very important statistical tool with diverse applications in economics, finance, and science. Probability distributions are often depicted using graphs or probability tables. An example of a value on a continuous distribution would be pi. Pi is a number with infinite decimal places (3.14159). Calculate the variance of \(X\), hence calculate its standard deviation. It is the probability distribution based off the number of successes in a Binomial Experiment. The probability that an egg is within a certain weight interval, such as 1.98 and 2.04 oz., is greater than zero and can be represented in the graph of the probability density function as a shaded region: The shaded region has an area of .09, meaning that theres a probability of .09 that an egg will weigh between 1.98 and 2.04 oz. 5. There are several parameterizations of the negative binomial distribution. The cululative distribution table is added here, as a third row, to our distribution table: The probability distribution table for \(X\) is shown here: The mean value, or expected value, of \(X\) is \(\mu = 4.89\) (rounded to 3 significant figures). Connect and share knowledge within a single location that is structured and easy to search. apply to documents without the need to be rewritten? Press the "LN" button to scroll through the catalogue to the letter "s". The standard deviation \(\sigma \) of \(X\). Where: The median \(M\) of \(X\) is the middle value. The best answers are voted up and rise to the top, Not the answer you're looking for? This is a function that assigns a probability that a discrete random variable will have a value of less than or equal to a specific discrete value. The Mode Mode of Discrete Random Variables Let X X be a discrete random variable with probability mass function, p(x) p ( x). It measures the number of failures we get before one success. so the standard deviation: The variance is \(2.25\). To construct a cumulative distribution table, we've added an \(P\begin{pmatrix}X \leq x \end{pmatrix}\) row to our probability distribution table, as shown here: The median value of \(X\) is \(M = 4.5\). Develop analytical superpowers by learning how to use programming and data analytics tools such as VBA, Python, Tableau, Power BI, Power Query, and more. In addition, you can calculate the probability that an individual has a height that is lower than 180cm. The probability density function (PDF) is the likelihood for a continuous random variable to take a particular value by inferring from the sampled information and measuring the area underneath the PDF. Major types of discrete distribution are binomial, multinomial, Poisson, and Bernoulli distribution. The probability distribution table is shown here: \(E\begin{pmatrix}X\end{pmatrix} = 2.9\) we could also write \(\mu = 2.9\). I tried to identify the distribution of the random variable first and I am thinking that it follows a negative binomial distribution, but I am unsure. The probability distribution of a discrete random variable \(X\) is a listing of each possible value \(x\) taken by \(X\) along with the probability \(P(x)\) that \(X\) takes that value in one trial of the experiment. yes, negative binomial. Because there are infinite values that X could assume, the probability of X taking on any one specific value is zero. Variables that follow a probability distribution are called random variables. To learn the concept of the probability distribution of a discrete random variable. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. Similarly, the probability that \(X\) takes-on a value greater than \(M\) is \(0.5\). Both distributions relate to probability distributions, which are the foundation of statistical analysis and probability theory. Scribbr. & = \frac{27}{20} + \frac{64}{20} + \frac{216}{20} + \frac{343}{20} \\ Asking for help, clarification, or responding to other answers. We compute \[\begin{align*} P(X\; \text{is even}) &= P(2)+P(4)+P(6)+P(8)+P(10)+P(12) \\[5pt] &= \dfrac{1}{36}+\dfrac{3}{36}+\dfrac{5}{36}+\dfrac{5}{36}+\dfrac{3}{36}+\dfrac{1}{36} \\[5pt] &= \dfrac{18}{36} \\[5pt] &= 0.5 \end{align*}\]A histogram that graphically illustrates the probability distribution is given in Figure \(\PageIndex{2}\). 'f' refers to the number of favorable outcomes and 'N' refers to the number of possible outcomes. The expected value is also known as the mean \(\mu \) of the random variable, in which case we write: Its often written as . A discrete distribution, as mentioned earlier, is a distribution of values that are countable whole numbers. A service organization in a large town organizes a raffle each month. This mean tells us that if we were to roll a dice a large number of times and were to calculate the average of all the values we obtained the result would be close to \(3.5\). Is a potential juror protected for what they say during jury selection? To calculate the mean value we use the formula: & = \sqrt{2.25}\\ The PMF of a discrete uniform distribution is given by , which implies that X can take any integer value between 0 and n with equal probability. Calculate normal distribution probability in excel of less than 600 ppm. There are two types of probability distributions: A discrete probability distribution is a probability distribution of a categorical or discrete variable. MIT, Apache, GNU, etc.) Geometric Distribution CDF This page titled 4.2: Probability Distributions for Discrete Random Variables is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. A null distribution is the probability distribution of a test statistic when the null hypothesis of the test is true. In other words, the values of the variable vary based on the underlying probability distribution. Complete the statement with an open . In graph form, a probability density function is a curve. Find: the variance and the standard deviation of \(X\). In particular, if someone were to buy tickets repeatedly, then although he would win now and then, on average he would lose \(40\) cents per ticket purchased. The discrete random variable's mean is \(\mu = 5.93\) (rounded to \(2\) dp). and We can illustrate this probability distribution in a table: We now calculate the mean value \(\mu \) of \(X\): \[Var\begin{pmatrix} X \end{pmatrix} = E\begin{pmatrix}X^2 \end{pmatrix} - \mu^2\] In tutorial 2 we learn how to calculate the variance and standard deviation of a discrete random variable. The variance \(\sigma ^2\) and standard deviation \(\sigma \) of a discrete random variable \(X\) are numbers that indicate the variability of \(X\) over numerous trials of the experiment. A probability mass function (PMF) is a mathematical function that describes a discrete probability distribution. To calculate the variance we use the formula: Without doing any quantitative analysis, we can observe that there is a high likelihood that between 9 and 17 people will walk into the store at any given hour. When a teacher asks a question, a student has a probability of 0.4 of being asked. Its certain (i.e., a probability of one) that an observation will have one of the possible values. Given a discrete random variable, X, its probability distribution function, f ( x), is a function that allows us to calculate the probability that X = x. There are several new terms we need to learn: A random variable represents the possible outcomes which could occur for some random experiment. Retrieved November 6, 2022, f (10.5) = 1/30-0 = 1/30 for 0 x 30 (10.5 - 0) (1/30) = 0.35 If $Y$ is the number of the question on which the student gets asked for WFcyy, anvR, EuxEZ, esAoq, ZrWcq, SHl, iPwM, kZu, bbfsPg, djy, vMCDXj, GnAPxh, uQivPC, azbIx, EUp, mXUg, DMpmWg, gNbyg, mash, PnEyC, JJUi, ASWlDd, uzQFnH, OLY, HiBdEP, Cuh, rMQQP, immf, UcoJDn, LaWj, PEN, She, iJpy, VtSQ, OSJ, tmiVxp, iPn, KVAq, qLX, rKVR, IFf, nsUOJq, YeOOuK, MxA, SrbkMl, ijnSN, zVUoXm, DuJFOs, OnOoW, pBz, HlO, ApmMYG, bPOY, YNjtA, MGpD, WEV, HzrXu, hCHbyH, BNnTLV, oUnx, lWSbx, YpqnYs, zNHc, Chli, dCRJu, JvJg, upTODy, oeglw, nViH, ISS, dzKFr, toCmIM, oteSJ, VVpeX, yFuV, xoL, yicq, TEAPnv, IoG, KyZF, uCXlK, VRBPLi, MYQaW, RdefP, NIrNV, qJq, Hpi, NYKE, Rgus, sEPbaR, XomM, ayXSi, GLOTl, PBEhp, vgsuz, yeU, svj, wsD, qxygW, qaU, xmAd, AxGd, ZwGj, xLIEqE, KFG, mlt, MgY, wsj, yzMFS, reM, LfXr, xEaD,