A random variable R has probability density,

p_R(x) = (x^m / m!)e^-x if x >= 0; and 0 otherwise

where m is a positive integer.

(a) Show that

P(0 <= R <= 2(m + 1)) = 1 - P(|R - (m + 1)| > m + 1)

(b) Use Chebyshev's inequality and part (a) to prove that

P(0 <= R <= 2(m + 1)) > m/m + 1