Probability and Statistics
Assignment No. 4
1. Let X be a continuous random variable with density function given by
fX(x) = 2(x + 1)/9 ,
-1 < x < 2
= 0,
otherwise.
Find the density function of Y = X2.
2. Let X be continuous random variable with density gi

Probability and Statistics
Assignment No. 5
1. Let (X,Y) have the joint pdf f(x,y) = e-(x+y) , x > 0, y > 0. Find P(1 < X+Y < 2),
P(X < YX < 2Y), P(0 < X < 1Y = 2). Determine such that P(X+Y < m) = .
2. Let (X,Y) have the joint pdf f(x,y) = x+y, 0 < x < 1

Probability and Statistics
Assignment No. 6
1. Let (X,Y) have the joint pmf
Y\ X
-2
1
2
-1
1/6
1/6
1/12
0
1/12
1/12
0
1
1/6
1/6
1/12
Find the joint pmf of (U,V) where U = X and V = Y2.
2. Projectiles are fired at the origin of an XY coordinate system. Ass

Probability and Statistics
Hints/Solutions to Assignment No. 4
1.
The range of Y is 0 to 4. For 0 y 1, there are two inverse images
y . For 1 < y < 4, there is one inverse image
density of Y as
2 1/2
f Y (y)
y,
0 y 1,
=
9
1
(1 + y 1/2 ), 1 < y < 4,
=
9
e

Probability and Statistics
Hints/Solutions to Assignment 5
1. P(1 < X + Y < 2) = 2 e-1 3 e-2. P( X < Y | X < 2Y ) = ,
P(0 < X < 1|Y = 2) = 1 e-1. P(X + Y < m) = , gives m as a solution of
2(m+1) = em, or approximately 1.6784.
2. The marginal distributions