1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Statistics - bivariate density calculations

  1. Oct 21, 2011 #1
    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
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted