Chapter 8: Q162S (page 452)

Given that xis a hypergeometric random variable, compute $p (x)$ for each of the following cases:
a. N= 8, n= 5, r= 3, x= 2
b. N= 6, n= 2, r= 2, x= 2
c. N= 5, n= 4, r= 4, x= 3

Short Answer

Expert verified

a. The probability distribution $p (x)$ is 0.5357.

b. The probability distribution $p (x)$ is 0.2.

c. The probability distribution $p (x)$ is 0.8.

Step by step solution

Given information

X is a hypergeometricrandom variable.

Computing the probability p(x) when N = 8, n = 5, r = 3, x = 2

For a hypergeometric random variable, the probability distribution

$p (x) = \frac{(\begin{matrix} r \\ x \end{matrix}) (\begin{matrix} N - r \\ n - x \end{matrix})}{(\begin{matrix} N \\ n \end{matrix})}$

Here $N = 8, n = 5, r = 3, x = 2$

$p (x) = \frac{(\begin{matrix} r \\ x \end{matrix}) (\begin{matrix} N - r \\ n - x \end{matrix})}{(\begin{matrix} N \\ n \end{matrix})} = \frac{(\begin{matrix} 3 \\ 2 \end{matrix}) (\begin{matrix} 8 - 3 \\ 5 - 2 \end{matrix})}{(\begin{matrix} 8 \\ 5 \end{matrix})} = \frac{(\begin{matrix} 3 \\ 2 \end{matrix}) (\begin{matrix} 5 \\ 3 \end{matrix})}{(\begin{matrix} 8 \\ 5 \end{matrix})} = \frac{3 \times 10}{56} = 0.5357$

Hence, the probability distribution $p (x)$ is 0.5357.

Computing the probability p(x) when N = 6, n = 2, r = 2, x = 2

Here $N = 5, n = 4, r = 4, x = 3$

$p (x) = \frac{(\begin{matrix} r \\ x \end{matrix}) (\begin{matrix} N - r \\ n - x \end{matrix})}{(\begin{matrix} N \\ n \end{matrix})} = \frac{(\begin{matrix} 2 \\ 2 \end{matrix}) (\begin{matrix} 6 - 3 \\ 2 - 2 \end{matrix})}{(\begin{matrix} 6 \\ 2 \end{matrix})} = \frac{(\begin{matrix} 3 \\ 2 \end{matrix}) (\begin{matrix} 4 \\ 0 \end{matrix})}{(\begin{matrix} 6 \\ 2 \end{matrix})} = \frac{3 \times 1}{15} = 0.2$

Hence, the probability distribution $p (x)$ is 0.2.

Computing the probability p(x) when N = 5, n = 4, r = 3, x = 3

Here, $N = 5, n = 4, r = 4, x = 3$

$p (x) = \frac{(\begin{matrix} r \\ x \end{matrix}) (\begin{matrix} N - r \\ n - x \end{matrix})}{(\begin{matrix} N \\ n \end{matrix})} = \frac{(\begin{matrix} 4 \\ 3 \end{matrix}) (\begin{matrix} 5 - 4 \\ 4 - 3 \end{matrix})}{(\begin{matrix} 5 \\ 4 \end{matrix})} = \frac{(\begin{matrix} 4 \\ 3 \end{matrix}) (\begin{matrix} 1 \\ 1 \end{matrix})}{(\begin{matrix} 5 \\ 4 \end{matrix})} = \frac{4 \times 1}{5} = 0.8$

Hence, the probability distribution $p (x)$ is 0.8.

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Sample 1	Sample 2
$n_{1} = 17 {\bar{x}}_{1} = 5.4 s_{1} = 3.4$	role="math" localid="1660287338175" $n_{2} = 12 {\bar{x}}_{2} = 7.9 s_{2} = 4.8$

Given that xis a hypergeometric random variable, compute $p (x)$ for each of the following cases:
a. N= 8, n= 5, r= 3, x= 2
b. N= 6, n= 2, r= 2, x= 2
c. N= 5, n= 4, r= 4, x= 3

Short Answer

Step by step solution

Given information

Computing the probability p(x) when N = 8, n = 5, r = 3, x = 2

Computing the probability p(x) when N = 6, n = 2, r = 2, x = 2

Computing the probability p(x) when N = 5, n = 4, r = 3, x = 3

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Given that xis a hypergeometric random variable, computep(x)for each of the following cases:a. N= 8, n= 5, r= 3, x= 2b. N= 6, n= 2, r= 2, x= 2c. N= 5, n= 4, r= 4, x= 3

Short Answer

Step by step solution

Given information

Computing the probability p(x) when N = 8, n = 5, r = 3, x = 2

Computing the probability p(x) when N = 6, n = 2, r = 2, x = 2

Computing the probability p(x) when N = 5, n = 4, r = 3, x = 3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Geometry

Probability and Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Given that xis a hypergeometric random variable, compute $p (x)$ for each of the following cases:
a. N= 8, n= 5, r= 3, x= 2
b. N= 6, n= 2, r= 2, x= 2
c. N= 5, n= 4, r= 4, x= 3