Let X and Y have the joint distribution given in Problem 1 of Chapter 3.
a. Find the covariance and correlation of X and Y .
b. Find E(Y |X = x) for x = 1, 2, 3, 4. Find the probability mass function of the random variable E(Y |X).
Reference
The joint frequency function of two discrete random variables, X and Y , is given in the following table:
a. Find the marginal frequency functions of X and Y .
b. Find the conditional frequency function of X given Y = 1 and of Y given X = 1.
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