Results 1 to 5 of 5

Math Help - Expeted value, Covarience help

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    16

    Expeted value, Covarience help

    I have a couple of exercise questions i'm having trouble with which any help would be much appreciated.

    1. Suppose N is exponentially distributed with parameter lambda. Given N, the R.V X has uniform distribution in the interval [0,N]. Evaluate E(X) and Var(X).

    I tried using E(X)=E[E(X|N)] and worked from their but confused myself...

    2.Suppose X and Y are independent standard normal variables. Let S=X+2Y and T=X-2Y.
    a)Evaluate Cov(S,T) and Cov(S-T,2S+T)
    b)Show that (S,T) has bivariate normal distribution

    For a), I worked out:
    Cov(S,T)=Cov(X+2Y,X-2Y)=Cov(X,X)+Cov(X,-2Y)+Cov(2Y,X)+Cov(2Y,-2Y)
    =Var(X)+0+0+2^2(Var(Y))=1+4=5
    Cov(S-T,2S+T)=Cov(4Y,3X+2Y)=Cov(4Y,3X)+Cov(4Y,2Y)
    =Cov(4Y,2Y)=I dont know
    b)I have no idea...

    Thanks in advance.
    Last edited by skirk34; May 27th 2009 at 05:17 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    May 2009
    Posts
    39
    the first question, i wonder the intever [0,N] or [0,T].
    the second, a) you can use cov(aX,bY) = ab cov(X,Y)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    16
    Quote Originally Posted by mahefo View Post
    the first question, i wonder the intever [0,N] or [0,T].
    the second, a) you can use cov(aX,bY) = ab cov(X,Y)
    My mistake, i changed it above, it is interval [0,N]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    First of all there are two ways of writing an exponential rv.
    It can be either

    {1\over \lambda}e^{-x/\lambda} or \lambda e^{-\lambda x}, the first has mean \lambda the other {1\over \lambda}.



    Next we have Cov(S-T,2S+T)=2V(S)-Cov(S,T)-V(T), yes that's a negative in front of a variance.
    From S=X+2Y and T=X-2Y, we have V(S)=1+4=5 and V(T)=1+4=5
    Cov(S,T)=Cov(X+2Y,X-2Y)=V(X)-4V(Y)=1-4=-3.

    Use MGFs or change variables, which isn't too hard here.
    The jacobian is just a constant so using the densities isn't a bad way to go.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2008
    Posts
    16
    Well, for Cov(S-T,2S+T) i simplified to
    Cov(4Y,3X+2Y)=Cov(4Y,3X)+Cov(4Y,2Y)
    since X and Y are independent, and standard normal RV
    Cov(4Y,3X)=0 and Cov(4Y,2Y)=(4*2)*Var(Y)=(8)*(1)=8

    Similarily, for Cov(S,T) i worked out to equal -3...

    I'm still a bit unsure on the other questions...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. covarience MATH EMERGENCY
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 20th 2010, 06:59 PM
  2. covarience
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 20th 2010, 06:53 AM

Search Tags


/mathhelpforum @mathhelpforum