Question: 4. Consider a random variable X with a moment generating function x (t) = E[etx]. (a) Show that for P[X a] x(t) eat

$4. Consider a random variable ( X ) with a moment generating function ( phi_{X}(t)=mathbb{E}left[e^{t X}ight] ). (a)$

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

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