Results 1 to 3 of 3

Math Help - help with random variable independence

  1. #1
    Senior Member
    Joined
    Sep 2009
    Posts
    300

    Unhappy help with random variable independence

    Let X~Bernoulli(θ) and Y~Geometric(θ), with X and Y independent. Let Z=X+Y. What is the probability function of Z?

    I am getting
    PX(1) = θ
    PX(0) = 1-θ
    PX(x) = 0 otherwise
    pY(y) = θ(1-θ)^y for y >= 0
    pY(y) = 0 otherwise


    What would PZ(z) be?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Sneaky View Post
    Let X~Bernoulli(θ) and Y~Geometric(θ), with X and Y independent. Let Z=X+Y. What is the probability function of Z?

    I am getting
    PX(1) = θ
    PX(0) = 1-θ
    PX(x) = 0 otherwise
    pY(y) = θ(1-θ)^y for y >= 0
    pY(y) = 0 otherwise


    What would PZ(z) be?
    read http://www.dartmouth.edu/~chance/tea...k/Chapter7.pdf
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Sep 2009
    Posts
    300
    i did that research and the only thing i could come up with is

    PX(X=1) = θPX(X=0) = 1-θPX(X=x) = 0 otherwise
    PY(Y=y>=0) = θ(1-θ)^y
    PY(Y=y) = 0 otherwiseso (X=k) and (Y=z-k) since Z = X+Y
    so

    PZ(Z=z)=

    summation from -inf to inf
    θ^2 * (1-θ)^(z-1)
    if x=1,y=1

    summation from -inf to inf
    θ * (1-θ)^(z+1)
    if x=0,y=0

    0
    otherwise


    Is this right?
    Last edited by Sneaky; October 23rd 2010 at 07:16 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 15th 2012, 11:37 PM
  2. Independence of random variables X and X^2
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 9th 2011, 04:22 AM
  3. Independence of Random Variables
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 18th 2011, 08:39 PM
  4. Replies: 9
    Last Post: January 28th 2010, 08:26 AM
  5. Replies: 3
    Last Post: January 13th 2010, 11:44 AM

Search Tags


/mathhelpforum @mathhelpforum