Let Z be a nonnegative random variable that satisfies E[Z^4]=4. Apply the Markov inequality to the random variable Z^4 to find the tightest possible (given the available information) upper bound on P(Z≥2).

Question

Let Z be a nonnegative random variable that satisfies E[Z^4]=4. Apply the Markov inequality to the random variable Z^4 to find the tightest possible (given the available information) upper bound on P(Z≥2).
P(Z>=2)<= ?E[Z^4]/2  = 2 But this is not the right answer

Anonymous · Accepted Answer

P(Z>=2) <= 0.25

PS-VP · Answer

How can the P(Z>2) be equal to 2? One of the axioms of Probability tells you that P(X)<=1