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Math Help - Probability and random random varible question

  1. #1
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    Joined
    Apr 2010
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    Probability and random random varible question

    Hi im not to sure how to show and work out these two questions? It would solve a great deal of problems if someone could help. Cheers

    Question 1) Recent astronomical observations indicate that, of the 20 stars closest to our sun,
    about half are accompanied by an orbiting planet at least the size of Jupiter.
    Assume that the proportion of such stars in the galaxy is 0.5. There is a group of 20 stars.

    Show that there is approximately an 8% chance of there being more than 13 or less
    than 6 with such a planetary system in such a group.

    also

    Question 2) Consider three random variables
    X, Y and Z which respectively represent the exam, skills test total and assignment scores (out of 100%) of a randomly chosen student.
    Suppose that past experience suggests the following properties of these assessment items
    (each out of 100%):

    E(X) = 55, sd(X) = 12
    E(Y) = 70, sd(Y) = 16
    E(Z) = 67, sd(Z) = 10
    .

    Find the distribution parameters,
    E(T) and Var(T), for the total mark, T=0.5X+0.32Y+0.18Z.
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  2. #2
    Junior Member
    Joined
    Mar 2010
    Posts
    28
    Q1) binomial dist (20,0.5)
    P(x>13) + P(x<6) = 0.08

    binomial dist is discrete
    P(x>13) = 1 - P(x<=13)
    P(x<6) = P(x<=5)

    use neave's table

    P(x>13) + P(x<6) = 1-0.9423 + 0.0207 = 0.0784, which is approx 8%

    Q2)
    T=0.5X+0.32Y+0.18Z, E(T) and Var(T)
    E(T) = 0.5*55+0.32*70+0.18*67 = 61.96
    Var(T)
    = (0.5^2)*(12^2)+(0.32^2)*(16^2)+(0.18^2)*(10^2)=
    65.4544

    hope it helps
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