Suppose that Y is a binomial random variable with n > 2

Chapter 3, Problem 55E

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QUESTION:

Suppose that  is a binomial random variable with \(n>2\) trials and success probability . Use the technique presented in Theorem  and the fact that \(E\{(Y-1)(Y-2)\}=E\left(Y^{3}\right)-3 E\left(Y^{2}\right)+2 E(Y)\) to derive \(E\left(Y^{3}\right)\).

Equation Transcription:

Text Transcription:

n>2

E{(Y-1)(Y-2)}=E(Y^3)-3E(Y^2)+2E(Y)

E(Y^3)

Questions & Answers

QUESTION:

Suppose that  is a binomial random variable with \(n>2\) trials and success probability . Use the technique presented in Theorem  and the fact that \(E\{(Y-1)(Y-2)\}=E\left(Y^{3}\right)-3 E\left(Y^{2}\right)+2 E(Y)\) to derive \(E\left(Y^{3}\right)\).

Equation Transcription:

Text Transcription:

n>2

E{(Y-1)(Y-2)}=E(Y^3)-3E(Y^2)+2E(Y)

E(Y^3)

ANSWER:

 Solution:

Step 1 of 3:

   Suppose that Y is a binomial random variable with n > 2 trials and success probability p.    

   Given equality

              

   Here we have to derive .


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