Discrete random variables Xu and Fu both take values in 101
     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

