= (a) [5 points] Consider now the tossing of a coin twice and let the following events be defined: A = {Heads on the fir

[answerhappygod]

A 5 Points Consider Now The Tossing Of A Coin Twice And Let The Following Events Be Defined A Heads On The Fir 1 (89.93 KiB) Viewed 82 times

= (a) [5 points] Consider now the tossing of a coin twice and let the following events be defined: A = {Heads on the first toss}, B = {Heads on the second toss}, C = {One head and one tail (in either order) is tossed}. Is the event collection {A, B, C} pairwise independent? Is it independent? Please justify your answer. (b) [5 points] Given a valid counterexample to disprove the equality "P(A|B) = P(B|A)". (c) [5 points] Consider a random variable X, with characteristic function 4x(t), finite mean EX = u and finite variance VarX = 02. Using Taylor expansion, show that as t 0, 1 4x(t) = 1 + itu – ezt? (x2 +02) +oct?). (d) [5 points] For random variables X~N(0,1) and W having the following discrete distribution: -1, with probablity 0.5, w 11, with probabilty 0.5. Assuming that X and W are independent, compute the Cov(x2,wx) and the P(WX <t) for some fixed t ER.