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5 June, 01:52

A manuscript is sent to a typing firm consisting of typists A, B and C. If it is typed by A, then the number of errors made is a Poisson random variable with mean 2.6; if typed by B then the number of errors made is a Poisson random variable with mean 3; and if typed by C then it is a Poisson random variable with mean 3.4. Let X denote the number of errors in the manuscript. Assume that each typist is equally likely to do the work. (a) Find E (X) (b) Find Var (X)

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  1. 5 June, 01:54
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    (a) E (X) = 3

    (b) Var (X) = 12.1067

    Explanation:

    (a) E[X]

    E[X]T = E[X]T=A + E[X]T=B + E[X]T=C

    = (2.6 + 3 + 3.4) / 3

    = 2.6 (1/3) + 3 (1/3) + 3.4 (1/3)

    = 2.6/3 + 1 + 3.4/3

    = 3

    (b) Var (X) = E[X²] - (E[X]) ²

    Recall that if Y ∼ Pois (λ), then E[Y 2] = λ+λ2. This implies that

    E[X²] = [ (2.6 + 2.6²) + (3 + 3²) + (3.4 + 3.4²) ]/3

    = (9.36 + 12 + 14.96) / 3

    = 36.32/3

    = 12.1067

    Var (X) = E[X²] - (E[X]) ²

    = 12 - 3²

    = 12.1067 - 9

    = 3.1067
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