NATIONAL UNIVERSITY OF SINGAPORE

Department of Statistics and Applied Probability

2014/2015 ST 3246 Statistical Models for Actuarial Science Semester I

Assignment 1

Due Date : 4 September 14 (Thursday) by 2 p.m.

Name:

Answer the following questions and submit your answers in IVLE before the due date.Incorrect answers will be marked for partial credit. For this purpose, you should show yourworking clearly in the spaces provided.

The cdf F (x) of a random variable X is given by

F (x) =

0, x < 0,

(x/B)a, 0 x < B,1, x B,

where a and B are constants.

Making use of the pair of constants a and B listed against your matriculation number in thefile HW1supp.pdf, calculate (rounding your answers to two decimal places):

1. E(X)

2. Var(X)

3. e(25)

4. E[(X 50)+]5. E(X 75)

1