Answers to Section 20 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 20.

Answer 20.1a. 1/10= 0.1

Answer 20.1b. 9/100= 0.09

Answer 20.1c. 9^k-1/10 ^k

Answer 20.2. about 0.387420489

Answer 20.3. about 0.9158381456

Answer 20.4a. 0.001999

Answer 20.4b. 1000 times

Answer 20.5a. 3/64= 0.046875

Answer 20.5b. 1/256= 0.00390625

Answer 20.6. about 0.3595464678

Answer 20.7a. P(X=3) = 4/27= about 0.148148148148; P(X=50) = about 7.84164273*10^-10

Answer 20.7b. E(X) = 3

Answer 20.8a. P(X = n) = (0.15)ⁿ(0.85) for all whole-number values of n.

Answer 20.8b. P(Y = n) =(0.15)^n-1(0.85) for all natural-number values of n.

Answer 20.9a. about 0.1198380223

Answer 20.9b. about 0.3998629849

Answer 20.11. about 0.0527265219

Answer 20.12a. 10

Answer 20.12b. 0.81

Answer 20.13a. X is a geometric distribution with pmf p(x) = 0.4(0.6)^x-1; x = 1, 2, etc.

Answer 20.13b. X is a binomial random variable with pmf p(x) = C(20, x)(0.60)^x(0.40)^20-x,

where x = 0, 1, ... , 20.

Answer 20.14. 108/625= 0.1728

Answer 20.15. 96/3125= 0.03072

Answer 20.16a. C(n-1, 2)(1/13)³(12/13)^n-3

Answer 20.16b. about 0.017934507

Answer 20.17. E(X)= 24; Var(X)= 120

Answer 20.18. 7/64= 0.109375

Answer 20.19. 3/16= 0.1875

Answer 20.20. 0.289792

Answer 20.21. 0.0221184

Answer 20.22a. about 0.1198380223

Answer 20.22b. about 0.0253527238

Answer 20.23. 20

Answer 20.24. about 0.0644972544

Answer 20.25. C(t-1, 2)(1/6)³(5/6)^t-3

Answer 20.26. 1625/4998= about 0.325130052

Answer 20.27. 1911/9614= about 0.1987726233

Answer 20.28. P(X=k)= C(6, k)*C(47, 6-k)/C(53, 6), for k= 0, 1, 2, 3, 4, 5, or 6

Answer 20.29. 80/323= about 0.2476780186

Answer 20.30. about 0.0727151097

Answer 20.31a. 3/14= 0.2142857143

Answer 20.31b. mean=3 batteries; Var(X)= 3/7= about 0.4285714286

Answer 20.32. 6149/7752= about 0.7932146543

Answer 20.33. C(2477,3)*C(121373, 97)/C(123850, 100)

Answer 20.34. 1/30= about 0.0333333333333333

Answer 20.35. about 0.2880

Answer 20.36. x = 4

Answer 20.37. 3/8 = 0.375

Answer 20.38. about 0.956

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