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Math Help - Statistics Question (Probability)

  1. #1
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    Statistics Question (Probability)

    Hi I dont really get the following so thanks if anyone could help:


    A biased cubical die has faces numbered 1, 2, 3, 4, 5, 6 and X denotes the number obtained when the die is tossed once with probabilities P(X = x) = kx^2.

    Find the value of k.

    Ten independent observations of X are taken. Find the probability that there is exactly four times when the result is at least 5.
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  2. #2
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    Quote Originally Posted by margaritas View Post
    Hi I dont really get the following so thanks if anyone could help:


    A biased cubical die has faces numbered 1, 2, 3, 4, 5, 6 and X denotes the number obtained when the die is tossed once with probabilities P(X = x) = kx^2.

    Find the value of k.
    As sum_{x=1 to 6} P(X=x) =1, we have to have:

    sum_{x=1 to 6} kx^2 =1

    so:

    k [1 + 4 + 9 + 16 + 25 + 36] = 1,

    so k = 1/91.

    Ten independent observations of X are taken. Find the probability that there is exactly four times when the result is at least 5.

    The probability that one one throw the result is at least 5 is

    P(X=5)+P(X=6) = (1/91) (25 + 36) = 61/91.

    The number of times this occurs in 10 trials has a binomial distribution B(10, 61/91), so the required probability is:

    b(4; 10, 61/91) = [10!/(4! 6!) (61/91)^4 (30/91)^6 ~= 0.054

    RonL
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