Two components of a minicomputer have the following 5.1 Jointly Distributed Random Variables 211 a. b. c. What is the joint pmf of X and Y? What is the probability that at most one error is made on both exams combined? Obtain a general expression for the probability that the total number of errors in the two exams is m (where m is a nonnegative integer). [Hint: A 5 {(x, y): x 1 y 5 m} 5 {(m, 0), (m 2 1, 1), . . . , (1, m 2 1), (0, m)}. Now sum the joint pmf over (x, y) [ A and use the binomial theorem, which says that om 1m2akbm2k 5 (a 1 b)m k50 k joint pdf for their useful lifetimes X and Y: 5xe2x(11y) x $ 0 and y $ 0 a. b. c. What is the probability that the lifetime X of the first component exceeds 3? What are the marginal pdf’s of X and Y? Are the two lifetimes independent? Explain. What is the probability that the lifetime of at least one component exceeds 3?

For problems 7–10, state a reasonable domain for the problem statement, find the inverse functionf –1(x), and identify the independent and dependent quantities of the inverse. gary is jogging. the total distance he has traveled, in miles, can be estimated using the functionf(x) = 9x, where x is his jogging time in hours. camryn sells computers. she earns commission for her computer sales plus a fixed wage for each day she works. her daily earnings, in dollars, can be estimated using the functionf(x) = 0.15x + 50, where x represents her computer sales in dollars. the distance a motorboat travels, in meters, can be estimated using the equation f(x) = 1.9x2, wherexisthetimeinseconds,for0≤x≤10. a rock band is selling tickets to a concert at a theater. the band earns money for each ticket sold, but has to pay some of the earnings to the theater. the total money earned by the band can be estimated using the function f(x) = 7.5x – 300, where x is the number of tickets sold.