(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)
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...
Related questions
Question
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feaf0af2a-3abd-4b05-8a4d-6ad3e8b11589%2F0aa33542-6119-4bf0-a7d1-d9ff81181f0e%2Fmrbovz4_processed.png&w=3840&q=75)
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).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON