QUESTION 5
In a hypergeometric random variable X, there are repeated trials of an event; however these are not independent.
This corresponds closely to the case of selecting marbles from a bowl (without replacement).
10 points
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The random variable X counts the number of marbles of category A out of N trials
There are two parameters: n, the number of trials; N, the total number of marbles, and $p = k/N$, the initial proportion of marbles of category A, (however, the probability of a
marble of category A varies after the first trial.
For example:
Select 4 marbles from a group of 15 marbles, of which 6 are red and 9 are other colors.
Let X = number of red marbles selected
a. Find the probability mass function for X:
$X=x$
$P(X=x)$
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b. Find E(X) and Var(X).