Suppose that X1 and X2 are independent Bernoulli trials each with probability 1/2, and let X3 =
Question:
a) Show that X1, X2, and X3 are pair wise independent, but X3 and X1 + X2 are not independent.
b) Show that V (X1 + X2 + X3) = V (X1) + V (X2) + V (X3).
c) Explain why a proof by mathematical induction of Theorem 7 does not work by considering the random variables X1, X2, and X3.
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a The probabilities that X 1 X 2 X 3 X 1 X 2 X 3 are as follows because with probability 1 we have that X 3 X 1 X 2 mod 2 We must show that X 1 and X ...View the full answer
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Related Book For 
Discrete Mathematics and Its Applications
ISBN: 978-0073383095
7th edition
Authors: Kenneth H. Rosen
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