Question

1. Three couples and two single individuals have been invited to an investment seminar and agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.4. (Any couple drives in the same car so they are either both late or both on time.) Assume that different couples and individuals arrive independently of one another. Let X = the number of people who arrive late for the seminar. a. Determine the pmf of X (Hint: label the three couples #1, #2, #3, and the individuals #4, #5). b. Obtain the cdf function of X, and use it to calculate P(2 SX 36) 2. Starting at a fixed time, each car entering an intersection is observed to see whether it turns left (L), right (R), or goes straight ahead (A). The experiment terminates as soon as a car is observed to turn left. Let X = the number of cars observed. What are the possible values, x, that X can take on? Give three possible outcomes and their associated x. 3. Starting at a fixed time, each car entering an intersection is observed to see whether it turns left (L), right (R), or goes straight ahead (A). The experiment terminates as soon as a car is observed to turn left. Let X = the number of cars observed. What are the possible values, x, that X can take on? Give three possible outcomes and their associated X 4. An insurance company offers its policyholders several different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows: 10 1.30 1.40 F(x) = .45 x<1 15x<3 35x<4 4 SX<6 65x< 12 12 SX .60 a. What is the pmf of X? b. Using just the cdf, compute P(35 X 5 6). C. Using just the cdf, compute P(43 X). d. Using just the cdf, compute P(4< X).

Answer 1

solution 4

Soluti n Lee x has cdf FA) 2 0 30 o40י a pmt at x is successic differchic bepa df cdf of x 12 0 30 b) P(3x6) = PexsS)-PCxs3) +Px 3) f(6)-Fxa)tPl3) e 06-cto. /PC3XE6)= 0.3 c) PC4x2-P(x4) -1- P(xe4) tf(x4) =1- FA)+R (4) = 1-d5 to-05 d PC1ex) = PC(x>4) = 1-xs4) = 1-frt4) = 1-0.45 PC4X)=S