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Expectation and Variance Consider a discrete random variable X whose probability mass function is defined by p(x)=P[X=x]={k1x20ifx{1,0,1}otherwise. Problem 2. Answer the following questions (recall that you need to show your work). (a) Determine the value of k that makes the above p(x) a valid probability mass function. (b) What is the expectation of X, i.e., compute E[X] ? (c) What is the expectation of X2, i.e., compute E[X2] ? (d) What is E[aX+b], where a,b are constants? (e) The variance of a random variable is the expected squared distance to its mean. Mathematically, it is Var(X)=E[(XE[X])2] Compute the variance of X, i.e., Var(X)