15. Given f[s.y)=3x for [l 5 y 5 it 51., find a. Rot) 1:. E0?) c. yams) d. Coy(X,Y) l. Assume that any result produced by a certain routine will be faulty 1with probability [IL]1 independently. What is the probability that a sample of three 1will have at most 1 faulty reSUlt? 1?. Suppose the number of bugs in a routine has a Poisson Distribution 1with parameter i=1. What's the probability that a routine has at least one bug? 13. What is the distribution of the sum of two i.i.cl. Poisson Distributions? Let K ~PoisU't} and Y~Pois{h]. Let Z=X+Y. Then P(Z=z]=P(K+Y=z)=? 19. A bag contains 11 pairs of shoes; each pair is a different style. You pick three random shoes from the bag. a. What is the probability of having a pair of shoes among the three you picked? b. What is the probability there is at least one left and at least one right shoe among the. Tl"| ref-.7