48. For any event A, we define the random variableI mage, called the indicator variable for A, by letting it equal 1 when A occurs and 0 when A does not. Now, ifI mage is a nonnegative random variable for allI mage, then it follows from a result in real analysis called Fubini's theorem that Suppose that X is a nonnegative random variable and that g is a differentiable function such thatI mage.

(a) Show that Image

(b) Show that Image where Image.