Answers to Section 27 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 27

Answer 27.1. about 0.1238883826

Answer 27.2. E(X)=3/2=1.5; Var(X)= ¾= 0.75

Answer 27.3. about 0.0947578682

Answer 27.4. about 0.4191864763

Answer 27.5. about 0.014387678

Answer 27.6a. f(x)= (1/16)x²e^-0.5x, x ≥ 0, 0 otherwise;E(X)= 6 million kilowatt hours.

Answer 27.6b. P(X>12)= ₁₂^∞∫(1/16)x²e^-0.5xdx

Answer 27.7. 480

Answer 27.8a. k=60

Answer 27.8b. E(X)= 4/7= about 0.5714285714; Var(X)= 3/98= about 0.0306122449

Answer 27.9a. F(X)=

0 for x

3x²-2x³ for 0 ≤ x ≤ 1,

1 for x > 1

Answer 27.9b. 99/250= 0.396

Answer 27.10a. f(x)= 60x³(1-x)² for 0 < x < 1, 0 otherwise.

Answer 27.10b. F(X)=

0 for x ≤ 0,

60x³−120x⁴+ 60x⁵, for 0 < x < 1,

1 for x ≥ 1.

Answer 27.11. 0.47178

Answer 27.12a. f(x)= 43.6486021x^1.0952(1-x)^4.6648, for 0 < x

Answer 27.12b. about 0.0829070132

Answer 27.13a. k=12

Answer 27.13b. 0.6875= 11/16

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