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(i) Demonstrate that F(x) is a valid cumulative distribution function. (ii) Determine a corresponding probability density function f(x) which describes the distribution. (iii) Determine the value of E[g(X)] when g(X) = X + 1. (iv) Use the result of the previous question to show that E(X)=1/5. %3D (v) Use the result of the previous question, and also that E[(X +1)²] = 3/2, to determine var(X).

(i) Demonstrate that F(x) is a valid cumulative distribution function. (ii) Determine a corresponding probability density function f(x) which describes the distribution. (iii) Determine the value of E[g(X)] when g(X) = X + 1. (iv) Use the result of the previous question to show that E(X)=1/5. %3D (v) Use the result of the previous question, and also that E[(X +1)²] = 3/2, to determine var(X).

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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just iv and v please thank you!

Consider a continuous random variable X described by the cumulative distribution function x < 0 F(x) = 1– (x + 1)–6 x > 0. (i) Demonstrate that F(x) is a valid cumulative distribution function. (ii) Determine a corresponding probability density function f(x) which describes the distribution. (iii) Determine the value of E[g(X)] when g(X)= X + 1. (iv) Use the result of the previous question to show that E(X) = 1/5. (v) Use the result of the previous question, and also that E[(X+1)²] = 3/2, to determine var(X).
Transcribed Image Text:Consider a continuous random variable X described by the cumulative distribution function x < 0 F(x) = 1– (x + 1)–6 x > 0. (i) Demonstrate that F(x) is a valid cumulative distribution function. (ii) Determine a corresponding probability density function f(x) which describes the distribution. (iii) Determine the value of E[g(X)] when g(X)= X + 1. (iv) Use the result of the previous question to show that E(X) = 1/5. (v) Use the result of the previous question, and also that E[(X+1)²] = 3/2, to determine var(X).
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