The graphs of the moment-generating functions of three

Chapter 3, Problem 16E

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QUESTION:

The graphs of the moment-generating functions of three normal distributions \(-N(0,1), N(-1,1)\), and \(N(2,1)\)-are given in Figure 3.3-3 (a). Identify them.

Equation Transcription:

Text Transcription:

−N(0,1),N(−1,1)

N(2,1)

Questions & Answers

QUESTION:

The graphs of the moment-generating functions of three normal distributions \(-N(0,1), N(-1,1)\), and \(N(2,1)\)-are given in Figure 3.3-3 (a). Identify them.

Equation Transcription:

Text Transcription:

−N(0,1),N(−1,1)

N(2,1)

ANSWER:

Answer:

Step 1 of 4:

          Given, the graph of the moment generating function of three normal distributions

                   N(0,1) , N(-1,1), N(2,1).

          For moment generating function of normal distribution is

                         (slope of line tangent to mgf at 0)


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