The possible values of $X$ are $0,1,2,\cdots, 9$. a. 3. Poisson Distribution The probability that the last digit of the selected number is 6, \begin{aligned} P(X=6) &=\frac{1}{10}\\ &= 0.1 \end{aligned}, b. \end{aligned} $$, Now, Variance of discrete uniform distribution X is,$$ \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=100.67-^2\\ &=100.67-100\\ &=0.67. The Discrete uniform distribution, as the name says is a simple discrete probability distribution that assigns equal or uniform probabilities to all values that the random variable can take. 4. All the integers $9, 10, 11$ are equally likely. A random variable $X$ has a probability mass function 2. Discrete Distributions Calculators HomePage Discrete probability distributions arise in the mathematical description of probabilistic and statistical problems in which the values that might be observed are restricted to being within a pre-defined list of possible values. 1. This list has either a finite number of members, or at most is countable. Let the random variable $X$ have a discrete uniform distribution on the integers $9\leq x\leq 11$. \end{aligned} $$, eval(ez_write_tag([[250,250],'vrcacademy_com-banner-1','ezslot_9',127,'0','0']));a. Let X denote the number appear on the top of a die. Let X denote the last digit of randomly selected telephone number. All rights are reserved. All the integers 0,1,2,3,4,5 are equally likely. b. Below are the few solved examples on Discrete Uniform Distribution with step by step guide on how to find probability and mean or variance of discrete uniform distribution. Discrete Random Variable Calculator Online probability calculator to find expected value E (x), variance (σ 2) and standard deviation (σ) of discrete random variable from number of outcomes. Code to add this calci to your website Discrete Random Variable's expected value,variance and standard deviation are calculated easily. This list has either a finite number of members, or at most is countable. (adsbygoogle = window.adsbygoogle || []).push({}); Discrete probability distributions arise in the mathematical description of probabilistic and statistical problems in which the values that might be observed are restricted to being within a pre-defined list of possible values. Find the mean and variance of X. 4 of theese distributions are available here. A discrete random variable has a discrete uniform distribution if each value of the random variable is equally likely and the values of the random variable are uniformly distributed throughout some specified interval. The probability that the number appear on the top of the die is less than 3 is,$$ \begin{aligned} P(X < 3) &=P(X=1)+P(X=2)\\ &=\frac{1}{6}+\frac{1}{6}\\ &=\frac{2}{6}\\ &= 0.3333 \end{aligned} $$a. which is the probability mass function (pmf) of discrete uniform distribution. If you continue without changing your settings, we'll assume that you are happy to receive all cookies on the vrcacademy.com website. This website uses cookies to ensure you get the best experience on our site and to provide a comment feature.$$ \begin{aligned} E(X^2) &=\sum_{x=9}^{11}x^2 \times P(X=x)\\ &= \sum_{x=9}^{11}x^2 \times\frac{1}{3}\\ &=9^2\times \frac{1}{3}+10^2\times \frac{1}{3}+11^2\times \frac{1}{3}\\ &= \frac{81+100+121}{3}\\ &=\frac{302}{3}\\ &=100.67. Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter $a$ and $b$. Discrete uniform distribution calculator can help you to determine the probability and cumulative probabilities for discrete uniform distribution with parameter a and b. c. Find the probability that $X\leq 6$. A discrete random variable $X$ is said to have uniform distribution with parameter $a$ and $b$ if its probability mass function (pmf) is given byeval(ez_write_tag([[580,400],'vrcacademy_com-medrectangle-3','ezslot_4',126,'0','0'])); $$f(x; a,b) = \frac{1}{b-a+1}; x=a,a+1,a+2, \cdots, b$$, $$P(X\leq x) = F(x) = \frac{x-a+1}{b-a+1}; a\leq x\leq b$$, The expected value of discrete uniform random variable $X$ is, The variance of discrete uniform random variable $X$ is, A general discrete uniform distribution has a probability mass function, Distribution function of general discrete uniform random variable $X$ is, The expected value of above discrete uniform random variable $X$ is, The variance of above discrete uniform random variable $X$ is. Let the random variable $X$ have a discrete uniform distribution on the integers $0\leq x\leq 5$. In general, PX()=x=px(), and p can often be written as a formula. Suppose $X$ denote the number appear on the top of a die. The mean μ of a discrete random variable X is a number that indicates the … \end{aligned} $$,$$ \begin{aligned} V(X) &= E(X^2)-[E(X)]^2\\ &=9.17-[2.5]^2\\ &=9.17-6.25\\ &=2.92. Then the mean of discrete uniform distribution $Y$ is, \begin{aligned} E(Y) &=E(20X)\\ &=20\times E(X)\\ &=20 \times 2.5\\ &=50. \end{aligned}, Mean of discrete uniform distribution $X$ is, \begin{aligned} E(X) &=\sum_{x=9}^{11}x \times P(X=x)\\ &= \sum_{x=9}^{11}x \times\frac{1}{3}\\ &=9\times \frac{1}{3}+10\times \frac{1}{3}+11\times \frac{1}{3}\\ &= \frac{9+10+11}{3}\\ &=\frac{30}{3}\\ &=10. Using the Binomial Probability Calculator b. The mean of discrete uniform distribution X is, \begin{aligned} E(X) &=\frac{4+8}{2}\\ &=\frac{12}{2}\\ &= 6. Let the random variable $X$ have a discrete uniform distribution on the integers $9\leq x\leq 11$. The probability that the last digit of the selected telecphone number is less than 3, \begin{aligned} P(X < 3) &=P(X\leq 2)\\ &=P(X=0) + P(X=1) + P(X=2)\\ &=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1+0.1\\ &= 0.3 \end{aligned}, c. The probability that the last digit of the selected telecphone number is greater than or equal to 8, \begin{aligned} P(X\geq 8) &=P(X=8) + P(X=9)\\ &=\frac{1}{10}+\frac{1}{10}\\ &= 0.1+0.1\\ &= 0.2 \end{aligned}. Then the random variable $X$ take the values $X=1,2,3,4,5,6$ and $X$ follows $U(1,6)$ distribution. \end{aligned} $$. To understand more about how we use cookies, or for information on how to change your cookie settings, please see our Privacy Policy. b. As the given function is a probability mass function (pmf), we have,$$ \begin{aligned} & \sum_{x=4}^8 P(X=x) =1\\ \Rightarrow & \sum_{x=4}^8 k =1\\ \Rightarrow & k \sum_{x=4}^8 =1\\ \Rightarrow & k (5) =1\\ \Rightarrow & k =\frac{1}{5} \end{aligned} $$, Thus the probability mass function (pmf) of X is,$$ \begin{aligned} P(X=x) =\frac{1}{5}, x=4,5,6,7,8 \end{aligned} . Continuous Uniform Distribution Calculator, Weibull Distribution Examples - Step by Step Guide, Karl Pearson coefficient of skewness for grouped data.

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