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Sum of binomial random variables

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data

    let y_1 and y_2 be iid bin(5,1/4) random variables

    let v=y_1+2*y_2 and u = 3*y_1 -2y_2

    find f_uv (u,v) and the cov(u,v)

    2. Relevant equations

    f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5

    covariance=E(uv)-E(u)E(v)

    3. The attempt at a solution

    By convolution the Sum of bin(n,p) and bin(m,p) = bin (n+m,p)

    so pdf of v = bin(15,1/4) and pdf of u = bin (5,1/4)

    The only way I know of to get the joint pdf is by a table. Is there a faster way?
     
  2. jcsd
  3. Nov 4, 2012 #2

    haruspex

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    For clarity, it's better to use the standard typecase: uppercase for names of r.v.s and lower case for values they take.
    When U = u and V = v, what can you say about the values of Y1 and Y2?
     
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