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 {$$ f(x,y) = c\frac{x}{y} $$}

*(10 pts)*Find*c*.*(5 pts)*f(1,1).*(10 pts)*Find F(x,y).*(5 pts)*Find F(1,1).*(5 pts)*Find F(1.5,1.5).*(5 pts)*Find F(2,2).*(10 pts)*Find the marginal pdf of X.*(10 pts)*Find the marginal pdf of Y.*(10 pts)*Find the marginal cdf of X.*(10 pts)*Find the marginal cdf of Y.*(10 pts)*Find E[X].*(10 pts)*Find E[Y].*(10 pts)*Find Var[X].*(10 pts)*Find Var[Y].*(10 pts)*Find COV[X,Y].*(10 pts)*Find the correlation coefficient of X and Y.*(10 pts)*Are X and Y independent?