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Suppose we toss a fair coin twice. Let X = the number of heads, and Y...

Suppose we toss a fair coin twice. Let X = the number of heads, and Y = the number of tails. X and Y are clearly not independent.

a. Show that X and Y are not independent. (Hint: Consider the events “X=2” and “Y=2”)

b. Show that E(XY) is not equal to E(X)E(Y). (You’ll need to derive the pmf for XY in order to calculate E(XY). Write down the sample space! Think about what the support of XY is and find those probabilities.)

Math   Statistics-And-Probability   
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