ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute

Homework 8, due 2pm Tues April 20

The random experiment is selecting a point from the square 1<=x<=2 and 1<=y<=2. However the points are not uniformly distributed, in fact the pdf {$$ f(x,y) = c\frac{x}{y} $$}

1. (10 pts) Find c.
2. (5 pts) f(1,1).
3. (10 pts) Find F(x,y).
4. (5 pts) Find F(1,1).
5. (5 pts) Find F(1.5,1.5).
6. (5 pts) Find F(2,2).
7. (10 pts) Find the marginal pdf of X.
8. (10 pts) Find the marginal pdf of Y.
9. (10 pts) Find the marginal cdf of X.
10. (10 pts) Find the marginal cdf of Y.
11. (10 pts) Find E[X].
12. (10 pts) Find E[Y].
13. (10 pts) Find Var[X].
14. (10 pts) Find Var[Y].
15. (10 pts) Find COV[X,Y].
16. (10 pts) Find the correlation coefficient of X and Y.
17. (10 pts) Are X and Y independent?