Solution Found!
Refer to Exercise 5.117. Suppose that the number N of
Chapter 5, Problem 121E(choose chapter or problem)
Refer to Exercise 5.117. Suppose that the number \(N\) of alligators in the population is very large, with \(p_{1}=.3\) and \(p_{2}=.1\).
a. Find the probability that, in a sample of five alligators, \(Y_{1}=2\) and \(Y_{2}=1\)
b. If \(n=5\), find \(E\left(\frac{Y_{1}}{n}-\frac{Y_{2}}{n}\right)\) and \(V\left(\frac{Y_{1}}{n}-\frac{Y_{2}}{n}\right)\)
Questions & Answers
QUESTION:
Refer to Exercise 5.117. Suppose that the number \(N\) of alligators in the population is very large, with \(p_{1}=.3\) and \(p_{2}=.1\).
a. Find the probability that, in a sample of five alligators, \(Y_{1}=2\) and \(Y_{2}=1\)
b. If \(n=5\), find \(E\left(\frac{Y_{1}}{n}-\frac{Y_{2}}{n}\right)\) and \(V\left(\frac{Y_{1}}{n}-\frac{Y_{2}}{n}\right)\)
Step 1 of 4
a) We have to find the probability of 5 alligators when \(Y_{1}=2\) and \(Y_{2}=1\)
Given that \(p_{1}=0.3\) and \(p_{3}=0.1\)
The pmf of multinomial distribution is
\(P\left(y_1,\ y_2,\ -y_k\right)=\frac{n!}{y_1!y_2!...y_k!}p_1^{y_1}p_2^{y_2\ldots\ldots}p_k^{y_k}\)