Exam 3: Discrete Random Variables and Probability Distributions

A chemical supply company currently has in stock 100lb of a certain chemical, which it sells to customers in 5-lb lots. Let X = the number of lots ordered by a randomly chosen customer, and suppose that X has pmf x 1 2 3 4 P(x) .2 .3 .3 .2 Compute E(X) and V(X). Then compute the expected number of pounds left after the next customer's order is shipped, and the variance of the number of pounds left. (Hint: The number of pounds left is a linear function of X.)

Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order, let X = the number among the first 6 examined that have a defective compressor. Compute the following: a. $P$ (X = 1) b. $P ( X \geq 4 )$