Another jpoint distribution problem

Quote:

Originally Posted by **braddy**

*problem 2:*

**A traffic engineer is studying the number of vehicles that arrive, during a certain 2-minute period, at two streets corners that are close to each other. Let X be the number of vehicles at on street corner and Y the number at the other. The enginner knows the joint distribution probability distribution of X and Y is:**

**-f(x,y)=(9/16)*(1/4)^(x+y), x=0,1,2,3..., y=0,1,2,....**

**- 0 elsewhere**

**For example P(X=1,Y=1)=0.035.**

**The enginner calculated E(X)=E(Y)=1/3, and Var(X)=Var(Y)=4/9.**

**He has calculated that X and Y are independent.**

I'm not sure what is being asked here. The X and Y are independent

can be deduced form:

f(x,y)= g(x)g(y), x=0,1,.. y=0,1, ..

where g(x)=(3/4)(1/4)^x since g(x) is a probability distribution, and as

the joint distribution is the product of marginal distributions for X and Y,

X and Y are independent.

Quote:

**1-Find rho, the correlation coefficient of X and Y.**

From the book, I get the formula

rho=E(((X-mean1)/var1)*((X-mean2)/var2))

but when I tried to compute it, I get undefined.

rho= sum_{x=1 to infty, y=1 to infty} (x-xbar)(y-ybar)/sqrt(var(x)var(y)) f(x,y)

but this sum is seperable to:

rho= [sum_{x=1 to infty} (x-xbar)/sqrt(var(x)) g(x)][sum_{y=1 to infty} (y-ybar)/sqrt(var(y)) g(y)] = 0

RonL