What is the probability distribution function for a hypergeometric distribution?

What is the probability distribution function for a hypergeometric distribution?

• A. f(x) = e^-λ*λ^x/x!
• B. f(x) = Pr(X=x) = C(m1,x) * C(m2,n-x)
• C. f(x) = p(1-p)^x
• D. f(x) = 1 - e^-λ

Answer: (B)

The probability distribution function for a hypergeometric distribution is correctly represented by the formula that involves combinations, specifically the product of combinations for two different groups. In the case of a hypergeometric distribution, we are interested in the number of successes (denoted by x) in a certain number of draws (n) from a finite population that contains a known number of successes (m1) and failures (m2). The formula states that the probability of obtaining exactly x successes in n draws is given by: \[ Pr(X=x) = \frac{C(m1, x) \times C(m2, n-x)}{C(m1 + m2, n)} \] Where: - \(C(m1, x)\) is the number of ways to choose x successes from the m1 successes available in the population. - \(C(m2, n-x)\) is the number of ways to choose the remaining n-x failures from the m2 failures available. - The denominator normalizes the probability by considering all possible outcomes of drawing n items from the total population of size \(m1 + m2\). This accurately reflects the nature of the hypergeometric distribution, which is used in scenarios where sampling is done without

The probability distribution function for a hypergeometric distribution is correctly represented by the formula that involves combinations, specifically the product of combinations for two different groups. In the case of a hypergeometric distribution, we are interested in the number of successes (denoted by x) in a certain number of draws (n) from a finite population that contains a known number of successes (m1) and failures (m2).

The formula states that the probability of obtaining exactly x successes in n draws is given by:

[

Pr(X=x) = \frac{C(m1, x) \times C(m2, n-x)}{C(m1 + m2, n)}

]

Where:

• (C(m1, x)) is the number of ways to choose x successes from the m1 successes available in the population.

• (C(m2, n-x)) is the number of ways to choose the remaining n-x failures from the m2 failures available.

• The denominator normalizes the probability by considering all possible outcomes of drawing n items from the total population of size (m1 + m2).

This accurately reflects the nature of the hypergeometric distribution, which is used in scenarios where sampling is done without