1. Suppose random variable X has the following probability distribution: a. Find E(X) and =V(X). b. If Y-5X+10, find E(Y) and V(Y). c. Find E(2X*+5). 2. It is found that a certain type of modem fails to connect (communicate) to the host computer on an average of 1 in every 5 attempts (logins). (That is, P(failure in each attempt) .2.) a. What is the probability that a failure occurs on the 10th attempt? b. What is the probability that the first failure occurs on the 10th attempt? c. What is the probability that the first failure occurs after the 20th attempt? d. What is the probability that the third failure occurs on the 5th attempt? e. What is the probability that there are more than 5 failures in 20 attempts? f. Suppose we improve the quality of this modem so that it fails, on the average, 1 in every 1000 attempts. What is the approximate probability that we see no more than 4 failures among the next 4000 attempts? 3. A report indicates that 40% of the memory chips produced by a certain manufacturer are defective. A computer store has received a shipment of 20 memory chips from this manufacturer. a. What is the probability that at least 5 of the chips in this shipment are defective? b. What is the probability that majority of the chips in this shipment are no-defective? c. What is the probability that the number of non-defective chips in this shipment is at least twice as many as the number of defective chips? 4. A computer monitor assembly line, produces a total of 20 monitors each day, of which 8 are 15-inch monitors and the rest are 17-inch monitors. Suppose at the end of a production day, we select random sample of 4 monitors for inspections. a. What is the probability that there are at least one 15-inch monitor in the selected sample. b. What is the probability that there are more than 3 17-inch monitor in the selected sample. c. If X denotes the number of 17-inch monitors in the sample, identify the probability distribution of X and then find E(X) and V(X). 5. Accidents are occurring at an intersection, independently, at a constant rate of 5 accidents per year (per 12-month). a. What is the probability that we see more than 3 accidents during the next 6-month? b. Suppose just now there has been an accident, what is the probability that we have to wait at least 2 months to see the next accident