A personal computer manufacturer produces both desktop computers and notebook computers. The monthly proportions of customer orders received for desktop and notebook computers that are shipped within one weeks time can be viewed as the outcome of a bivariate random variable (X, Y) with joint probability density f( x, y) = (2 - x - y)I10,1J (x)l10,1J(Y)
a. In a given month, what is the probability that more than 75 percent of notebook computers and 75 per cent of desktop computers are shipped within one week of ordering?
b. Assuming that an equal number of desktop and notebook computers are ordered in a given month, what is the probability that more than 75 percent of all orders received will be shipped within one week?
c. Are the random variables independent?
d. Define the conditional probability that less than 50 percent of the notebook orders are shipped within one week, given that x proportion of the desktop orders are shipped within one week (the probability will be a function of the proportion x). How does this probability change as x increases?