Question: 20. Let the probability density function of a random variable X be f (x) = xn n! ex , x 0. Show that P

20. Let the probability density function of a random variable X be f (x) = xn n! e−x , x ≥ 0. Show that P (0 < X < 2n + 2) > n n + 1 . Hint: Note that # ∞ 0 xne−x dx = 0(n + 1) = n!. Use this to calculate E(X) and Var(X). Then apply Chebyshev’s inequality.

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20. Let the probability density function of a random variable X be Show that Use this to calculate E(X) and Var(X). Then apply Chebyshevs inequality. f(x) = x 0. n!

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