stats assignment 111, Assignments of Economics

Download stats assignment 111 and more Assignments Economics in PDF only on Docsity! Statistics for Economics : Assignment 4 1. SupposeX and Y are 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: ˆ E[X2Y ] ˆ E[X − Y ] ˆ V ar[X − Y ] ˆ ρXY ˆ 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) = { 250x if 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 X is as follows: f(x) = { e −x for x > 0 0 otherwise ˆ Find the pdf of Y = X1/2 (you may use the cdf technique) ˆ Find the pdf of W = X1/k 6. Suppose the pdf of X is as follows: 1