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)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35130480-ce61-412d-a9bb-70fe97997c47%2F3019ee90-b149-4d86-a417-d28cdf7c6eb5%2Fq3cn6x_processed.jpeg&w=3840&q=75)
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
\[ R''(0) = \text{Var}(X) = 0.2475. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35130480-ce61-412d-a9bb-70fe97997c47%2F3019ee90-b149-4d86-a417-d28cdf7c6eb5%2Fg2ahqta_processed.jpeg&w=3840&q=75)
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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