Question

2. A small pond contains 30 fish, 10 of which have been tagged. Suppose that a fisherman’s catch consists of four fish. (Assume that these four fish form a random sample of size four selected without 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 3 tagged fish.

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

Answer 1

Let denote the number of tagged fish that are caught.

a) The PMF of is

This distribution is called hyper geometric distribution.

b) The probability,

c) Here . The mean of the distribution is

The variance is