Q 2.8. Suppose that (X, Y) are bivariate random variables whose joint distribution is continuous with density f(x,y) (x, y) [xe-x(y+¹) if x,y>0, otherwise. = hồ By finding the conditional distribution of Y given X = x for x > 0, compute the conditional probability P(Y> 1 | X= 1).

A-c

Cynthia is president of an international chemical distribution company, Cchem. Weekly gross sales for Cchem has a mean of $1 million and standard deviation of $0.2 million; the distribution of sales is highly right-skewed. One week’s sales are independent of the sales in any other week. Use this information to answer questions 5 to 6 below. What is the probability that sales for the week of October 5, 2009 will be more than $1.25 million? In order for Cynthia to receive a bonus, Cchem’s annual sales must exceed $53 million. What is the probability that Cynthia will receive a bonus for the fiscal year starting in 2010? Assume there are 52 weeks in a year.

#4 A bowl contains 5 red beads, 6 blue beads, and 3 violet beads. If 3 beads are picked at random, without replacement, from the bowl, find the probability that (a) the first is red, the second is blue, and the third is violet (b) all 3 are red (c) the first is blue and the second and third are not blue (d) at least one is violet.