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Compute the expectation ex and variance varx of x as a

Let X be a random variable with range RX = {-1, 0, 1} and let P(X = 1) = P(X = -1) = p/2 for some p ∈ [0, 1].

a) Compute P(X = 0).

b) Compute the expectation E[X] and variance Var(X) of X as a function of p, and determine the value of p for which Var(X) becomes maximal.

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