Let X be a random variable with probability density function given by (z) = { 2(1 – 2), 0SISI 0, elsewhere a. Use the method of distribution functions to find the density function of U1 2Х- 1. b. Use the method of transformations to find the density function of U1 = 2X – c. Use the method of distribution functions to find the density function of U2
Let X be a random variable with probability density function given by (z) = { 2(1 – 2), 0SISI 0, elsewhere a. Use the method of distribution functions to find the density function of U1 2Х- 1. b. Use the method of transformations to find the density function of U1 = 2X – c. Use the method of distribution functions to find the density function of U2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please complete each portion
![Let X be a random variable with probability density function given by
f(x) = { 2(1 – 2), 0<I<1
0,
elsewhere
a. Use the method of distribution functions to find the density function of U1
2X – 1.
b. Use the method of transformations to find the density function of U1 = 2x-1.
c. Use the method of distribution functions to find the density function of U2 =
1- 2X.
d. Use the method of transformations to find the density function of U2 = 1–2X.
e. Use the method of distribution functions to find the density function of U3 =
X².
f. Find E(U3) using the density function got in part e, and compare it with the result
using E[U3] = Sr²f(x)dr](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9ad9a17-86a2-4d23-8aeb-c537a78d9db8%2Ff654190c-220d-4b83-9021-750d8cbcb205%2Foyhdtpj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X be a random variable with probability density function given by
f(x) = { 2(1 – 2), 0<I<1
0,
elsewhere
a. Use the method of distribution functions to find the density function of U1
2X – 1.
b. Use the method of transformations to find the density function of U1 = 2x-1.
c. Use the method of distribution functions to find the density function of U2 =
1- 2X.
d. Use the method of transformations to find the density function of U2 = 1–2X.
e. Use the method of distribution functions to find the density function of U3 =
X².
f. Find E(U3) using the density function got in part e, and compare it with the result
using E[U3] = Sr²f(x)dr
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