(a) find the probability density function fy(v). (b) find p( y 1) (c) find p(y1). (d) find e(y). 2. (10') for persons infected with a certain form of disease, the length of time spent in remission is described by the continuous pdf fy(y)-|y2, 0 y < 3, where y is m easured in years. (a) what is the average length of time that a patient spend in remission? (b) what is the probability that a patient's remission lasts longer than 2 years? 3. (10) a box is to be constructed so that its hight is 5 inches and its base is y inches by y gy-gy2,0 < y < 1 find inches, where y is a random variable describedby the pdf fy(y) the expected volume of the box 4. (10') suppose that on-the-job injuries in a textile mill occur at the rate of 0.1 per day. (a) what is the probability that two accidents will occur during the next (ive-day) work week? (b) if someone gets injured today, what is the probability that a week (ive days) or more will elapse before another injury occurs? 5. (10') in an experiment, probes land at random in the interval [0,2] on the r-axis. (a) what is the probability that a probe lands in the interval (0,1/21? (b) if three probes operate independently and lands, what is the probability that exactly two probes land in the interval [0, 1/2]? (150 lft y be a uniform random variable on the interval [2,3)