Discrete random variables X(u) and F(u) both take values in {-1,0,+1}. The joint probability
mass function for X (u) and Y (u) is where K is a constant. Find and provide a label sketch of
the conditional probability mass functions: Given that X(u) = i, find the best estimate of Y(u)
under the Linear MMSE, MMSE, Maximum Likelihood, and Maximum A posteriori Probability
criteria. Fill in the table below to describe your answer: What is the residual mean-squared error
for the Linear MMSE estimator?
Solution.
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Discrete random variables X(u) and F(u) both take values in {-1,0,+1}.pdf
1. Discrete random variables X(u) and F(u) both take values in {-1,0,+1}. The joint probability
mass function for X (u) and Y (u) is where K is a constant. Find and provide a label sketch of
the conditional probability mass functions: Given that X(u) = i, find the best estimate of Y(u)
under the Linear MMSE, MMSE, Maximum Likelihood, and Maximum A posteriori Probability
criteria. Fill in the table below to describe your answer: What is the residual mean-squared error
for the Linear MMSE estimator?
Solution
