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Thread: Probability function

  1. #1
    Nov 2009

    Probability function

    I am trying to solve the d, e and f parts of this problem
    The discrete random variable X has probability function
    where k is a positive constant.
    P(X = x) ={k(2 x), x = 0, 1, 2,
    k(x 2), x = 3,
    0, otherwise,
    (a) Show that k = 0.25.
    (b) Find E(X) and show that E(X 2) = 2.5.
    (c) Find Var(3X 2).
    Two independent observations X1 and X2 are made of X.
    (d) Show that P(X1 + X2 = 5) = 0.
    (e) Find the complete probability function for X1 + X2.
    (f) Find P(1.3 < X1 + X2 < 3.2).
    Not sure how to begin. Please help. The exam is tomorrow.
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  2. #2
    MHF Contributor
    May 2010
    (d)if X1+X2 = 5 then one of them must be 2, ie:
    X1=3, X2=2

    Show that the probability of X1=2 is 0, and likewise for X2.

    X1, X2 can be 0,1,3. There are only 9 possibilities for the combination. Calculate them all and hence the distribution of X1+X2.

    use the distribution you calculated in (e).
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