Please show all work when solving. Keep in mind Gaussian Random Variable when solving. Let \( X \) be a random variable with the moment-generating function (MGF) \( m(\theta) = e^{\theta^2} \), where the real part of \( \theta \), denoted as \( \text{Re}(\theta) \), belongs to the set of real numbers \( \mathbb{R} \). What is the probability density function (pdf) of \( X \)?

As Prof. A. M. Goon said "Let X be a random variable with probability function (probability mass…

Answered: Let X be a r.v. with the MGF m(0) =…

Math

Probability

Let X be a r.v. with the MGF m(0) = eª², Re(0) € R. What is the pdf of X?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Please show all work when solving.

Keep in mind Gaussian Random Variable when solving.

Let \( X \) be a random variable with the moment-generating function (MGF) \( m(\theta) = e^{\theta^2} \), where the real part of \( \theta \), denoted as \( \text{Re}(\theta) \), belongs to the set of real numbers \( \mathbb{R} \). What is the probability density function (pdf) of \( X \)?

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