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Assume that X is a discrete random variable with moment generating function defined on its domain as M(t) = 0.55e' +0.45. (a) Describe the probability distribution of X. You should list the name of the distribution and the associated defining parameter(s) of the distri- bution. 5.

Assume that X is a discrete random variable with moment generating function defined on its domain as M(t) = 0.55e' +0.45. (a) Describe the probability distribution of X. You should list the name of the distribution and the associated defining parameter(s) of the distri- bution. 5.

A First Course in Probability (10th Edition)
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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5. Assume that \( X \) is a discrete random variable with moment generating function defined on its domain as \[ M(t) = 0.55e^t + 0.45. \] (a) Describe the probability distribution of \( X \). You should list the name of the distribution and the associated defining parameter(s) of the distribution.
Transcribed Image Text:5. Assume that \( X \) is a discrete random variable with moment generating function defined on its domain as \[ M(t) = 0.55e^t + 0.45. \] (a) Describe the probability distribution of \( X \). You should list the name of the distribution and the associated defining parameter(s) of the distribution.
(b) Show that \( \text{Var}(X) = 0.2475 \). You may apply a formula presented in lecture for this distribution! (c) Let \( R(t) \) be defined as \[ R(t) = \ln(0.55e^t + 0.45). \] Show that \[ R''(0) = \text{Var}(X) = 0.2475. \]
Transcribed Image Text:(b) Show that \( \text{Var}(X) = 0.2475 \). You may apply a formula presented in lecture for this distribution! (c) Let \( R(t) \) be defined as \[ R(t) = \ln(0.55e^t + 0.45). \] Show that \[ R''(0) = \text{Var}(X) = 0.2475. \]
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