Asked by Logan Ann Moberly on Jun 12, 2024

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Given that n is the number of trials of a random experiment, N is population size, M is the number of population units with the "success" characteristic, and p is the probability of success in the first trial, the mean of the hypergeometric random variable's probability distribution always equals:

A) n
B) np
C) n(N/M)
D) none of these

Hypergeometric Random Variable

A discrete random variable that represents the count of successful outcomes in a series of selections from a limited population where each selection is not returned to the pool.

Probability of Success

The likelihood that an event will occur as desired, often represented as a number between 0 and 1.

Mean

The average of a set of numbers, calculated by dividing the sum of these numbers by the count of the numbers in the set.

  • Ascertain and clarify the average, variance, and alternate probabilities inherent in hypergeometric distribution scenarios presented.
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AA
Amanda Acosta [STUDENT]Jun 19, 2024
Final Answer :
B
Explanation :
The mean of the hypergeometric distribution is given by nMNn\frac{M}{N}nNM , which can be interpreted as npnpnp where p=MNp = \frac{M}{N}p=NM is the probability of success in a single trial.