Question: Continuous random variable (3) Let X be a continuous random variable with mean p, and standard deviation 0. Suppose that the density f X(:1:) is

Continuous random variable

(3) Let X be a continuous random variable with mean p, and standard deviation 0. Suppose that the density f X(:1:) is symmetric about u in the sense that fou + :13) = fXUL 33)- (a) Show that P(X g p, k) g % when k > 0. (b) Show that this inequality can fail without the symmetry assumption by considering an exponential distribution

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