Suppose that X I and X 2 are independent Bernoulli trials
Chapter 6, Problem 6.4.27(choose chapter or problem)
Suppose that X I and X 2 are independent Bernoulli trials each with probability 112, and that X 3 = (XI + Xz) mod 2. a) Show that XI , Xz, and X3 are pairwise independent, but X 3 and X I + X 2 are not independent. b) Show that V(XI + X2 + X3) = V(XJ) + V(X2) + V(X3). c) Explain why a proof by mathematical induction of Theorem 7 does not work by considering the random variables X], Xz, and X3.
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