7.6.1. You wish to measure random variable X with expected value E[X] = 1 and variance Var[X] = 1, but your measurement procedure yields the noisy observation Y = X +Z, where Z is the Gaussian (0, 2) noise that is independent of X. (a) Find the conditional PDF fzx(z|x) of Z given X =x. (b) Find the conditional PDF fyxy/2) of Y given X = 2. Hint: Given X = x, Y =x +Z.

7.6.1. You wish to measure random variable X with expected value E[X] = 1 and variance Var[X] = 1, but your measurement procedure yields the noisy observation Y = X +Z, where Z is the Gaussian (0, 2) noise that is independent of X. (a) Find the conditional PDF fzx(z|x) of Z given X =x. (b) Find the conditional PDF fyxy/2) of Y given X = 2. Hint: Given X = x, Y =x +Z.

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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7.6.1. You wish to measure random variable X with expected value E[X] = 1 and variance Var[X] =
%3D
1, but your measurement procedure yields the noisy observation Y = X +Z, where Z is the Gaussian
(0, 2) noise that is independent of X.
(a) Find the conditional PDF fzjx(z|x)of Z given X =x.
(b) Find the conditional PDF fyx(y/2) of Y given X = 2. Hint: Given X = x, Y = x +Z.

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