Problem 121E

Refer to Exercise 5.117. Suppose that the number N of alligators in the population is very large, with p1 = .3 and p2 = .1.

a Find the probability that, in a sample of five alligators, Y1 = 2 and Y2 = 1.

Reference

A population of N alligators is to be sampled in order to obtain an approximate measure of the difference between the proportions of sexually mature males and sexually mature females. Obviously, this parameter has important implications for the future of the population. Assume that n animals are to be sampled without replacement. Let Y1 denote the number of mature females and Y2 the number of mature males in the sample. If the population contains proportions p1 and p2 of mature females and males, respectively (with p1 + p2 < 1), find expressions for

Solution

Step 1 of 3

a) We have to find the probability of 5 alligators when Y1=2 and Y2=1

Given that and

The pmf of multinomial distribution is

Here we have to find

=

=

=0.0972

Hence the probability of 5 alligators when Y1=2 and Y2=1 is 0.0972