Answers to Section 16 of Marcel B. Finan's "A Probability Course for the Actuaries"
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.
See a list of all the answer keys to Dr. Finan's study guide for Exam 1/P here.
Section 16.
Answer 16.1a. 1/30= about 0.0333333333
Answer 16.1b. 10/3= about 3.33333333333333
Answer 16.1c. 127/15= about 8.466666666666667
Answer 16.2a. c=1/9
Answer 16.2b. p(-1)= 2/9, p(1)=1/3, and p(2)= 4/9.
Answer 16.2c. E(X)=1; E(X2) = 7/3= about 2.33333333333333
Answer 16.3a. p(x)=x/21 for x = 1, 2, 3, 4, 5, 6, and p(x) = 0 otherwise.
Answer 16.3b. 4/7= about 0.5714285714
Answer 16.3c. 13/3= about 4.33333333333
Answer 16.5. E(F(X))=0.62
Answer 16.6. The expected payment for hospitalization is $220 under this policy.
Answer 16.7. 43/1370= about 0.0313868613
Answer 16.8. 0.24
Answer 16.9a. p(x)=
4/7, for x= -1,
3/7 for x=2,
0 otherwise.
Answer 16.9b. E(2X)= 2
Answer 16.10a. P= 3C+ 8A+ 5S- 300
Answer 16.10b. $1,101
Answer 16.12. For n = 1, E(S) = 108. For n = 2, E(S) = 115.2. For n = 3, E(S) = 121.6.
See a list of all the answer keys to Dr. Finan's study guide for Exam 1/P here.
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5 Comments
Post a Comment16.12 is a binomial distribution with p=0.2 and q=(1-p)=0.8 so E(Y)=np and var(Y)=npq. then E(Y^2)=var(Y)+[E(Y)]^2.
Good morning. I was wondering how to calculate the answer for 16.5. My answer us 1.86 which is the expected value but I'm not sure what the next step is.
thanks for any assistance
Guys, Any hint for question 16.12. I am feeling difficulty to calculate value of E(Y) and E(Y2).
16.1b: ans 10/3 is correct.
E(X) = 1*c+2*4c+3*9c+4*16c
= 100*c
= 100*1/30
= 10/3
Good afternoon:
I have a question about 16.1b regarding finding the E(X)
the problem is p(x) = cx (with x squared)
and x = 1,2,3,4
c is a constant of 1/30...but I don't see how they got 10/3... any guidance would be appreciated