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Suppose X is a random variable such that $E[2^X] = 4$. Give an upper bound for P(X ≥ 3).

I know I must use Markov's inequality here: P(X ≥ a) = $\frac{E|X|}{a}$

For other problems I have solved I was given the expected value not as a function of X so I am unsure how to manipulate this in order to give the desired bound.

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$X \geq a$ iff $2^{X} \geq 2^{a}$. Hence $P(X \geq a)=P(2^{X} \geq 2^{a}) \leq \frac {E2^{X}} {2^{a}}=\frac 4 {2^{a}}$. Put $a=3$.

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