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CaptainBlack

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2. Let X be a random variable that follows a Uniform(0; 1) distribution.

(a) Show that E(X) = 1/2 and Var(X) = 1/12.

(b) Using Chebyshev's inequality find an upper bound on the prob-

ability that X is more than k standard deviations away from its

expected value.

(c) Compute the exact probability that X is more than k standard

deviations from its expected value.

( d) Compare the bound to the exact probability.Thanks