Let X be a continuous random variable with CDF F. Suppose that P(X > 0) = 1 and that JE(X) exists. Show that JE(X) = fOCXlJP'(X > x)dx. Hint: Consider integrating by parts. The following fact is...

Let X be a continuous random variable with CDF F. Suppose that P(X > 0) = 1 and that JE(X) exists. Show that JE(X) = fOCXlJP'(X > x)dx. Hint: Consider integrating by parts. The following fact is helpful: ifJE(X) exists then limX --+CXl x[l - F(x)] = O.