Question: 1. Let X be a random variable with Probability Density Function (PDF) and let YX. = 6x, if 0xa, fx(x) = -2x, if -ax0,

1. Let X be a random variable with Probability Density Function (PDF) and let YX. = 6x, if 0xa, fx(x) = -2x, if -ax0, 0, otherwise, (a) Determine the constant a such that fx (x) is a valid PDF. (b) Calculate E[X] and var(X) (c) Calculate E[Y] and var(Y) (d) Determine the Cumulative Distribution Function (CDF) of X, i.e., Fx(x) = P(X x).

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