Seja X uma vari´avel aleat´oria com a seguinte fun¸c˜ao de distribui¸c˜ao acumulada: F (x) =    0, se x < 10 1 5 , se 10 ≤ x < 15 3 5 , se...

(a) P(X ≤ 12) = F(12) = 1/5 (b) P(X = 23) = F(23) - F(23-) = 1 - 3/5 = 2/5 (c) E(X) = ∫xf(x)dx = ∫[10,15)5x/100 dx + ∫[15,23)3x/100 dx + ∫[23,∞)x/100 dx = 16.9 (d) Var(X) = E(X²) - [E(X)]² = ∫x²f(x)dx - [E(X)]² = ∫[10,15)5x²/100 dx + ∫[15,23)3x²/100 dx + ∫[23,∞)x²/100 dx - 16.9² = 29.41