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9. Let U be a uniform random variable on (0, 1), X be a Bernoulli random variable with success probability pe (0, 1), and X,U are independent. (a) Find the CDF of U + X. (b) Find the conditional PMF of U + X | U = u, where u e (0, 1). (c) Find the conditional PDF of U +X X = x, where a 0, 1.

9. Let U be a uniform random variable on (0, 1), X be a Bernoulli random variable with success probability pe (0, 1), and X,U are independent. (a) Find the CDF of U + X. (b) Find the conditional PMF of U + X | U = u, where u e (0, 1). (c) Find the conditional PDF of U +X X = x, where a 0, 1.

MATLAB: An Introduction with Applications
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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9. Let U be a uniform random variable on (0, 1), X be a Bernoulli random variable with success probability p E (0, 1), and X,U are independent. (a) Find the CDF of U + X. (b) Find the conditional PMF of U + X | U = u, where u e (0, 1). (c) Find the conditional PDF of U + X X = x, where r= 0, 1.
Transcribed Image Text:9. Let U be a uniform random variable on (0, 1), X be a Bernoulli random variable with success probability p E (0, 1), and X,U are independent. (a) Find the CDF of U + X. (b) Find the conditional PMF of U + X | U = u, where u e (0, 1). (c) Find the conditional PDF of U + X X = x, where r= 0, 1.
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