(5) A discrete random variable X has the probability mass function f(x) = c(x + 1)², x=-1,0, 1. You must show work when answering the following questions. (a) Determine the value of the constant c. (Please double check your answer. We will not give partial credit if you don't get this part right.) (b) Find the mean and the variance of X. (c) Give a formula or a sketch of F(x), the cumulative distribution function of X.
(5) A discrete random variable X has the probability mass function f(x) = c(x + 1)², x=-1,0, 1. You must show work when answering the following questions. (a) Determine the value of the constant c. (Please double check your answer. We will not give partial credit if you don't get this part right.) (b) Find the mean and the variance of X. (c) Give a formula or a sketch of F(x), the cumulative distribution function 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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![(5) A discrete random variable \( X \) has the probability mass function
\[
f(x) = c(|x|+1)^2, \quad x = -1, 0, 1.
\]
You must show work when answering the following questions.
(a) Determine the value of the constant \( c \). (Please double check your answer. We will not give partial credit if you don't get this part right.)
(b) Find the mean and the variance of \( X \).
(c) Give a formula or a sketch of \( F(x) \), the cumulative distribution function of \( X \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1941a39f-dbc9-477a-8528-f1bffe3dd4bc%2Fbf933a28-f386-4c7d-9813-1feadc44ed0e%2Fzbfkmu_processed.png&w=3840&q=75)
Transcribed Image Text:(5) A discrete random variable \( X \) has the probability mass function
\[
f(x) = c(|x|+1)^2, \quad x = -1, 0, 1.
\]
You must show work when answering the following questions.
(a) Determine the value of the constant \( c \). (Please double check your answer. We will not give partial credit if you don't get this part right.)
(b) Find the mean and the variance of \( X \).
(c) Give a formula or a sketch of \( F(x) \), the cumulative distribution function of \( X \).
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