Question

Reconsider the fish pond problem but this time suppose that the sample is selected with replacement. A small pond contains 50 fish, 15 of which have been tagged. Suppose that a fisherman catches five fish by catching a fish, noting whether it is tagged, releasing it, and repeating until five fish have been caught. (Assume that these five fish form a random sample of size five selected with replacement.) Let X denote the number of tagged fish that are caught.

a) What is the name of the distribution of X and what is the p.m.f. of X for this example? Provide an expression for pX(x).

b) Find the probability that the fisherman’s catch will contain at most 4 tagged fish.

c) Use the appropriate expressions from section 7.9 to compute expected value of X and the variance of X. 1

Answer 1