What are the pdf, the mean, and the variance of X if the

Chapter 3, Problem 1E

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QUESTION:

What are the pdf, the mean, and the variance of \(X\) if the moment-generating function of  \(X\) is given by the following?

(a) \(M(t)=\frac{1}{1-3 t}, \quad t<1 / 3\).

(b) \(M(t)=\frac{3}{3-t}, \quad t<3\).

Equation Transcription:

Text Transcription:

X

M(t)=1/1-3t, t<1/3

M(t)=3/3-t, t<3

Questions & Answers

QUESTION:

What are the pdf, the mean, and the variance of \(X\) if the moment-generating function of  \(X\) is given by the following?

(a) \(M(t)=\frac{1}{1-3 t}, \quad t<1 / 3\).

(b) \(M(t)=\frac{3}{3-t}, \quad t<3\).

Equation Transcription:

Text Transcription:

X

M(t)=1/1-3t, t<1/3

M(t)=3/3-t, t<3

ANSWER:

Answer

Step 1 of 3

The moment generating function M(t)=, t<

 For this pdf is f(t)=,t0


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