4-40. Let X be a continuous random variable whose mean E(X) = and varianceV( X) = 2 exist. For any > 0 and small,

4-40. Let X be a continuous random variable whose mean E(X) = μ and varianceV(

X) = σ2 exist. For anyε > 0 and small, verify that the (4.19) version of Chebyshev’s Theorem holds.

(Hint: start with V(X) = 4 +∞
−∞ (x − μ)2f (x)dx and let {X |−∞ < X < +∞} = {X |−∞ < X < μ− ε} ∪ {X |μ +ε < X < +∞}.)