A jar contains 7 red marbles, 5 blue marbles, and 3 green marbles. Consider the

Question

A jar contains 7 red marbles, 5 blue marbles, and 3 green marbles. Consider the following experiments using this jar:

(a) We draw 6 marbles from the jar, without replacement, and let X count the number of red marbles we draw.

(b) We draw marbles from the jar, with replacement, until we have drawn two red marbles, and let X count the number of blue marbles drawn.

(c) We draw marbles from the jar, without replacement, until we have drawn at least one of each color. Let X count the number of blue marbles drawn.

For each experiment, say if X has a named distribution (Bernoulli, Binomial, Geometric, Hypergeometric, or Negative Binomial) find the parameters if it is. I

Explanation / Answer

(a)

Here X has hypergeometric distribution with parameters

Population size: N = 7+5+3 = 15

Sample size: n = 6

Number of suceess is population: k=7

(B)

Since draws are done with replacement so probability of drawing red marble is each draw is p=7/15.

Here X has negative binomial distribution with parameters r=2 and p = 7/15.

(c)

Here X does not have any specific distribution.

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