Answers to Sections 18 and 19 of Marcel B. Finan's "A Probability Course for the Actuaries"

These answer keys are meant to assist students using Marcel B. Finan's A Probability Course for the Actuaries. With Dr. Finan's permission, Mr. Stolyarov wrote solutions for the problems in his study guide and is endeavoring to make the answer keys to each section publicly available. You can see his full List of Answer Keys here. Do the problems at the end of each section and then check your answers with these keys.

Dr. Finan's study guide is an excellent resource for those preparing to take Actuarial Exam 1/P on probability.

Problems that require numerical answers are answered here, but it is still the responsibility of the student to provide his or her own work for these problems. These answers are meant to enable students to independently verify the correctness of their reasoning by checking to see if the end result they obtained is correct. Questions from the study guide that require proofs or diagrams are not addressed here, as the end result of those questions is known in advance, and it is the responsibility of the student to provide the procedure for getting there.

Section 18.

Answer 18.1. 0.38263752

Answer 18.2. 27/128= 0.2109375

Answer 18.3. p(x)=

1/8, for x=0,

3/8, for x=1,

3/8, for x=2,

1/8 for x=3,

0 otherwise

Answer 18.4. about 0.0956576009

Answer 18.5. $60

Answer 18.6. 61/1250= 0.0488

Answer 18.7. about 0.9245163262

Answer 18.8. about 0.1441136931

Answer 18.9a. 3/16= 0.1875

Answer 18.9b. 0.5= ½

Answer 18.10. about 0.1198380223

Answer 18.11. about 0.6241903616

Answer 18.12. about 1.82284263*10^-5

Answer 18.13. SD(X)= about 0.6324523697

Answer 18.14. E(X²)= 154

Answer 18.15. 0.135

Answer 18.16. 0.784

Answer 18.17a. about 0.2321

Answer 18.17b. about 0.2649

Answer 18.17c. about 0.1238

Answer 18.18. about 0.2639

Section 19.

Answer 19.1. e^{- 4}=about 0.0183156389= probability of no car accident in one day. 8e^-8= about 0.002683701= probability of 1 car accident in two days.

Answer 19.2. About 0.1251100357= probability of receiving 10 calls in 5 minutes.

Answer 19.3. e^-15 = about 3.059023205*10^-7= probability of having no errors on a page.

Answer 19.4a. about 0.5768099189

Answer 19.4b. e^-3 = about 0.0497870684

Answer 19.5a. about 0.9473469827

Answer 19.5b. about0.7618966944

Answer 19.5c. about 0.160623141

Answer 19.6. about 0.761897

Answer 19.7a. 1- e^-5/6=about 0.5654017915

Answer 19.7b. about 0.4963317258

Answer 19.8. about 0.4231900811

Answer 19.9. λ= variance= 2

Answer 19.10. about$7231.30

Answer 19.11.about$698.90

Answer 19.12. about 0.1550277818

Answer 19.13. about 0.758563549

Answer 19.14. λ = 4

Answer 19.15a. about 0.2873

Answer 19.15b. about 4.47

Answer 19.16. about 0.0838

See a list of all the answer keys to Dr. Finan's study guide for Exam 1/P here.