Math 3339 EMCF Homework 4 Sections 4.3 - 4.8 Honework will NOT be accepted through email or in person. Homework must be submitted through CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under \"EMCF\" and choose ehw4. For problems 1 - 4 name the type of probability distribution that can be used for each case. 1. Of all customers purchasing automatic garage door openers, 75% purchase a chain-driven model. Let X = the number among the next 15 purcharsers who select the chain-driven model. a. b. c. d. e. Poisson Geometric Binomial Hypergeometric None of these 2. Draw marbles from a bag containing 5 red marbles, 6 bule marbles and 4 green marbles without replacement and count the number of blue marbles. a. b. c. d. e. Hypergeometric Geometric Binomial Poisson None of these 3. Draw marbles from a bag containg 5 red marbles, 6 blue marbles and 4 green marbles with repacement until you get a blue marble. a. b. c. d. e. Hypergeometric Geometric Binomial Poisson None of these 4. Draw marbles from a bag containing 5 red marbles, 6 bule marbles and 4 green marbles with replacement and count the number of blue marbles. a. b. c. d. e. Hypergeometric Geometric Binomial Poisson None of these 1 The following table is a joint probability table for X = number of dogs a person owns and Y = number of cats a person owns. Use this to answer questions 5 - 9. Y 0 0.20 0.08 0.15 0 1 2 X 1 0.05 0.15 0.02 2 0.10 0.12 0.13 5. What is the probability P (X = 0, Y = 0)? a. b. c. d. e. 0.43 0.35 0.20 0.4651 0.5714 6. What is the probability that a person owns one cat, given they own one dog? a. b. c. d. e. 0.6818 0.4286 0.1500 0.2200 0.3500 7. Is \"number of dogs\" and \"number of cats\" independent? a. Yes b. No 8. How many dogs does a person expect to own? a. b. c. d. e. 1 0.02 0.95 0.92 0.35 2 9. Give the conditional probability distribution of number of dogs, given that they have one cat. a. X P(X | Y = 1) 0 0.08 1 0.15 2 0.12 b. X P(X | Y = 1) 0 0.43 1 0.22 2 0.35 c. X P(X | Y = 1) 0 0.186 1 0.682 2 0.343 d. X P(X | Y = 1) 0 0.229 1 0.429 2 0.343 e. None of these 10. What is the total number of cats and dogs that a person is expected to own? a. b. c. d. e. 2 1.87 0.935 1 None of these 3 Use this information to answer questions 11 - 14: The number of requests for assistance received by a towing service is a Poisson process with rate of 4 per hour. 11. What is the probability that exactly ten requests are received during a particular 2-hour window? a. b. c. d. e. 0.0053 0.0993 0.8159 0.9972 none of these 12. What is the probability that at most ten requests are received during a particular 2-hour window? a. b. c. d. e. 0.0053 0.0993 0.8159 0.9972 none of these 13. If the operator of the towing service take a 30-minute break for lunch, what is the probability that they do not miss any calls for assistance? a. b. c. d. e. 0.1353 0.0183 0.0003 0.8647 none of these 14. How many calls would you expect during their 30-minute break? a. b. c. d. e. 4 2 8 16 none of these 15. An urn contains 3 green balls, 2 blue balls, and 4 red balls. In a random sample of 5 balls, find the probability that at least one blue balls is selected. a. b. c. d. e. 1 6 5 6 7 9 5 18 5 9 4