Assignment 3, Stat 633
Rabab Elnaiem
September 27, 2015
1
Problem 1:
a. Develop an accept-reject algorithm to generate from the Beta(a, b) distribution (assume a >
1, b > 1). Use U nif orm(0, 1) as the instrumental density, and derive the optimal value of

Homework 3: Stat 433/633, Fall 2015
Due: Monday, September 28, 2015
1. (a) Develop an accept-reject algorithm to generate from the Beta(a, b) distribution (assume
a > 1, b > 1). Use Uniform(0, 1) as the instrumental density, and derive the optimal
value o

Assignment 2, Stat 633
Rabab Elnaiem
September 21, 2015
1
Problem 1:
Draw a random sample of size 105 from the N (0, 1) distribution using the approximate method
of generating 12 uniform variables as discussed in class. Plot a histogram of the sample with

Homework 2: Stat 433/633, Fall 2015
Due: Monday, September 21, 2015
1. Draw a random sample of size 105 from the N (0, 1) distribution using the approximate method
of generating 12 uniform variables as discussed in class. Plot a histogram of the sample wi

Homework 1: Stat 433/633, Fall 2015
Due: Monday, September 14, 2015
Instructions: Please see the syllabus for guidelines on writing up homework. Show your work
clearly.
1. Problem given in class about Monte Carlo estimation of the standard normal cumulati

Assignment 1, Stat 633
Rabab Elnaiem
September 14, 2015
1
Problem 1:
Completing the standard normal CDF through Monte Carlo estimation :
m
10
102
103
104
105
exact
Table 0.1: standard normal CDF.
t
0
0.67
0.84
1.28
0.7
0.6
0.9
0.8
0.55
0.64
0.81
0.92
0.52