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Math Help - binominal probability

  1. #1
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    binominal probability

    A particular sale involves four items randomly selected from a large lot that is known to contain 10% defectives. let Y denote the number of defectives among the four sold. the purshaser of the items will return the defectives for repair, and the repair cost is given by C=3Y^2+Y+2
    find the expected repair cost.
    where do i start?
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  2. #2
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    Quote Originally Posted by mathlovet View Post
    A particular sale involves four items randomly selected from a large lot that is known to contain 10% defectives. let Y denote the number of defectives among the four sold. the purshaser of the items will return the defectives for repair, and the repair cost is given by C=3Y^2+Y+2
    find the expected repair cost.
    where do i start?
    E(C) = 3 E(Y^2) + E(Y) + 2 where Y ~ Binomial(n = 4, p = 1/10).

    A binomial distribution can be assumed because, although it's sampling without replacement, the population is large.

    Note that E(Y^2) = Var(Y) + [E(Y)]^2.
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