Compute the Mean and Standard Deviation of a Hypergeometric Random Variable
-In a lottery, a player must choose 6 numbers between 1 and 36 inclusive. Six balls are then randomly selected from an urn containing 36 balls numbered from 1 to 36 . The random variable $X$ represents the number of matching numbers. What are the mean and standard deviation of the random variable $X$ ?
A) $\mu _ { X } = 1.000 , \sigma X = 29.580$
B) $\mu \mathrm { X } = 1.000 , \sigma \mathrm { X } = 0.913$
C) $\mu _ { X } = 0.167 , \sigma X = 29.580$
D) $\mu _ { X } = 0.167 , \sigma X = 0.913$

Question

Quizplus · Accepted Answer

The mean of a hypergeometric random variable is given by $\mu _ { X } = n p$ and the standard deviation is given by $\sigma X = \sqrt { n p q ( 1 - p / N ) } $, where $n$ is the number of draws, $p$ is the probability of success on each draw, $q = 1 - p$, and $N$ is the total number of objects in the population. In this case, $n = 6$, $p = 1 / 6$, $q = 5 / 6$, and $N = 36$. Therefore, the mean is $\mu _ { X } = 6 \times 1 / 6 = 1.000$ and the standard deviation is $\sigma X = \sqrt { 6 \times 1 / 6 \times 5 / 6 \times ( 1 - 1 / 6 ) } = 29.580$.

Compute the Mean and Standard Deviation of a Hypergeometric Random XXX

Compute the Mean and Standard Deviation of a Hypergeometric Random $X$