Question: 4. (Total: 6 points) Consider a non-negative continuous random variable X with an unknown distribution. (a) (3 points) Derive the Markov's inequality regarding X,

4. (Total: 6 points) Consider a non-negative continuous random variable X with

4. (Total: 6 points) Consider a non-negative continuous random variable X with an unknown distribution. (a) (3 points) Derive the Markov's inequality regarding X, that is, for any positive constant c, E(X) Pr(X c) (b) (3 points) Show that for any positive constants c and t, Pr(Xc) eMx(t), where Mx(t) is the moment generating function of X.

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