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2 2. Suppose that X Uniform (0.5,1) and Y Bernoulli (x), that isk P(Y = 1|X = x) = x P(Y=0|X = x) = (1 − x) P(Y=y|X = x) = 0 when y # 0,1 a. Find P(Y = 0) and P (Y = 1) b. Find ƒ(X|Y)(X|Y = y) for y = 0,1 c. Find the MMSE estimate XM of X given Y d. Find the MSE for the estimator X you computed in c. M e. Find the linear MMSE estimate XL of X given Y.

2 2. Suppose that X Uniform (0.5,1) and Y Bernoulli (x), that isk P(Y = 1|X = x) = x P(Y=0|X = x) = (1 − x) P(Y=y|X = x) = 0 when y # 0,1 a. Find P(Y = 0) and P (Y = 1) b. Find ƒ(X|Y)(X|Y = y) for y = 0,1 c. Find the MMSE estimate XM of X given Y d. Find the MSE for the estimator X you computed in c. M e. Find the linear MMSE estimate XL of X given Y.

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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2. Suppose that X~ Uniform(0.5,1) and Y Bernoulli (x), that isk ~ P(Y= 1|X = x) = x P(Y=0|X = x) = (1-x) P(Y=y|X = x) = 0 when y = 0,1 a. Find P(Y = 0) and P (Y = 1) b. Find ƒ(X|Y)(X|Y = y) for y = 0,1 c. Find the MMSE estimate XM of X given Y d. Find the MSE for the estimator XM you computed in c. e. Find the linear MMSE estimate XL of X given Y.
Transcribed Image Text:2. Suppose that X~ Uniform(0.5,1) and Y Bernoulli (x), that isk ~ P(Y= 1|X = x) = x P(Y=0|X = x) = (1-x) P(Y=y|X = x) = 0 when y = 0,1 a. Find P(Y = 0) and P (Y = 1) b. Find ƒ(X|Y)(X|Y = y) for y = 0,1 c. Find the MMSE estimate XM of X given Y d. Find the MSE for the estimator XM you computed in c. e. Find the linear MMSE estimate XL of X given Y.
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