Let W be a random variable giving the number of heads minus the number of tails...

Let W be a random variable giving the number of heads minus the number of tails in three independent tosses of an unfair coin where p = P(H) = 1 3 , and q = P(T) = 2 3 . (a) List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value of W. (b) Find P(−1 ≤ W < 1). (c) Draw a graph of the probability density function f(t) of W, and the cumulative distribution function F(t). (d) Compute µW = E(W) and σ 2 W .

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