4. Consider a random variable X with a moment generating function x (t) = E[etx]. (a)...

 

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4. Consider a random variable X with a moment generating function x (t) = E[etx]. (a) Show that for P[X ≥ a] ≤ Øx(t) " eat any t≥ 0, a ER. (Hint:use Markov's inequality.) (b) Suppose X is normally distributed with mean μ and variance o². Show that P[X ≥u+a] ≤ exp a² (-2002) 9 for any a > 0. 4. Consider a random variable X with a moment generating function x (t) = E[etx]. (a) Show that for P[X ≥ a] ≤ Øx(t) " eat any t≥ 0, a ER. (Hint:use Markov's inequality.) (b) Suppose X is normally distributed with mean μ and variance o². Show that P[X ≥u+a] ≤ exp a² (-2002) 9 for any a > 0.