In the name of God, the Merciful, the Compassionate
Engineering Probability and Statistics
Department of Computer Engineering
Sharif University of Technology
Fall 2009 – CE 40-181
Homework #5 Due: 9/9/88
1- Solve the following problems from your text book:
5-13 5-14 5-21 5-26 5-27 5-28 5-35 5-50
2- Random variable X has pdf
Let Y =e X , find pdf of Y.
3- Random variable X has pdf
f X  x =
1
x e− x/  / 2 , 0x∞ ,  2 a positive constant.
2
f X  x =
2
nm1! n
x 1− xm ,0x 1, m, n positive
n ! m!
integers.
Let Y =−logX , find pdf of Y.
{
x−1
1 x3
4- If the random variable X has pdf f  x = 2
, find a monotone
0
otherwise
u

x

Y
=u
 x  has a uniform(0, 1)
function
such that the random variable
distribution.
5- A random right triangle can be constructed in the following manner. Let X be a
random angle whose distribution is uniform on 0,/2 . For each X, construct a
triangle as
Here, Y = height of the random triangle.
For a fixed constant d, find the distribution of Y . Also, find
E [Y ] .