Question: The density function of a random variable X is given by f (x) = 1 n! xnex, x > 0, where n is a positive

The density function of a random variable X is given by f (x) = 1 n!

xne−x, x > 0, where n is a positive integer. Show that P(X

n n + 1.

(Hint: Use the formula0 xke xdxk!, k = 0, 1,2...,

to find the mean and variance of X. Then, use Chebyshev’s inequality.)

0 xke xdxk!, k = 0, 1,2...,

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