# Statistics - bivariate density calculations

1. Oct 21, 2011

### XodoX

1. The problem statement, all variables and given/known data
Consider the bivariate density f(x,y)=c(x+y) for 0<=x<1, 0<=y<1

a) Obtain the appropriate normalization constant c.

b) Obtain the marginal densities for X and Y, and calculate their means and variances.

c) Obtain the covariance between X and Y, and check whether the random variables are independent.

d) Obtain the conditional distribution of Y, given that X=x

3. The attempt at a solution

a) Good question. I thought you double integrate the function, then you get c and then you solve it for c, but you can't solve it for c because there's no f(x,y) = whatever number. There needs to be something on the other side, too. No idea.

b)Double integrate the function using - and + infinity ? f(x)= ∫f(x,y)dy and f(y)=∫f(x,y)dx

No idea hoe to get the means and variances, though.

c) That is a tough one. Double integrate it again using this ? ∫∫ (x-μx)(y-μy)f(x,y)dxdy ( infinity for both ∫) ?

d) I know it's g(ylx)= f(x,y)/f1(x) and h(xly)=f(x,y) / F2(y)... Does this already imply X=x ? So I basically just divide the functions ?

Any help is appreciated! Thank you