Results 1 to 3 of 3

Math Help - stochastic independence and random variables

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    16

    stochastic independence and random variables

    Suppose X1 and X2 are stoch. indep. Bernoulli RVs with params p1 and p2 respectively. Let Y = X1X2 and W = X1 + X2. I need to determine whether the following statements are true or false so just give me a clue please, I'd like to work it out myself. If no tip can be given without giving it away please say so.
    1. the RV Y ~ Bernoulli(p_1p_2)

    --------
    2. What is the general formula for finding the variance of a RV of the form Z = XY (X and Y both RVs).

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2008
    Posts
    16
    here's what I got for my first question:
    E(Y) = E(X_1X_2) = E(X_1)E(X_2) = p_1p_2
    => true, since E(X) = p for RV ~ Bernoulli(p)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    16
    I found the formula for the second question.

    The problem wanted me to prove that given X,Y indep. and Z=XY
    V(Z)=E^2(X)V(Y) + E^2(Y)V(X)+V(X)V(Y)

    and the formula I found was
    V(XY)=E^2(X)V(Y) + E^2(Y)V(X)+V(X)V(Y)
    +2E(X)E(Y)Cov(X,Y)+Cov^2(X,Y)

    and from here the answer is obvious given that Cov(X,Y)=0.

    However, I'd like to know how the formula for V(XY) is derived.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Independence of random variables X and X^2
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 9th 2011, 03:22 AM
  2. Independence of Random Variables
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 18th 2011, 07:39 PM
  3. Replies: 6
    Last Post: November 16th 2009, 02:42 PM
  4. Proof of independence of random variables
    Posted in the Advanced Statistics Forum
    Replies: 10
    Last Post: September 28th 2009, 12:31 PM
  5. 3 Gaussian random variables, independence
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 12th 2007, 04:06 AM

Search Tags


/mathhelpforum @mathhelpforum