Differentiate the moment-generating function in Exercise

Chapter 3, Problem 146E

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QUESTION:

Differentiate the moment-generating function in Exercise 3.145 to find \(E(Y)\) and \(E\left(Y^{2}\right)\). Then find \(V(Y)\).

Equation Transcription:

Text Transcription:

E(Y)

E(Y^2)

V(Y)

Questions & Answers

QUESTION:

Differentiate the moment-generating function in Exercise 3.145 to find \(E(Y)\) and \(E\left(Y^{2}\right)\). Then find \(V(Y)\).

Equation Transcription:

Text Transcription:

E(Y)

E(Y^2)

V(Y)

ANSWER:

Solution:

Step 1:

Step 1 of 3:

Let Y has a binomial distribution with n trials and probability of success p.

We have to find E(Y) and E(by differentiating the moment generating function.

Then we have to find the variance V(Y).


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