45-733 PROBABILITY AND STATISTICS I Notes #5D
February 2000
f(x) = {1/[(2p)^{1/2} s]} e^{-(x - m)2/ 2s2)} -¥ < x < +¥
Where E(X) = m and VAR(X) = s^{2}_ _ _ _ P(X_{2} > Y_{3}) = P(X_{2} - Y_{3} > 0) _ Clearly X_{2} ~ N(625, 50) _ and Y_{3} ~ N(600, 50) _ _ so that X_{2} - Y_{3} ~ N(25, 100) _ _ Hence: P[(X_{2} - Y_{3} - 25)/10 > (0 - 25)/10] = P(Z > -2.5) = 1 - F(-2.5) = 1 - .0062 = .9938