Statistics for Economics : Assignment 4
1. Suppose Xand Yare continuous ransom variables with joint density f(x, y) = 4(x−xy)
if 0 <x<1 and 0 < y < 1 and zero otherwise. Then calculate:
E[X2Y]
E[X−Y]
V ar[X−Y]
ρXY
f(y|x) and E[Y|x]
2. Suppose there are 10 total balls of different colors in an urn and one of the color in
red. Now, I randomly draw one ball at a time with replacement. Find the expected
number of draw which should generate 3 red balls in consecutive draws?
3. Suppose f(x, y, z , t) is joint probability density function-
f(x, y, z, t) = {
1
xyz for 0 < t ≤z≤y≤x≤1
0 otherwise
Find fY,Z,T (y, z , t), fX,T (x, t),and fZ(z).
4. Suppose a woman owns 2 businesses and the profit from each business is independent
of each other. If the probability density function of weekly revenue from each business
is-
f(x) = {250xif 1 < x < 3
0 otherwise
Find the probability that difference between weekly revenue of both the business will
be more than 500 units.
5. Suppose the pdf of Xis as follows:
f(x) = {e−xfor x > 0
0 otherwise
Find the pdf of Y=X1/2(you may use the cdf technique)
Find the pdf of W=X1/k
6. Suppose the pdf of Xis as follows:
1
