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Math Help - Expected values

  1. #1
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    Question Expected values

    Silica Tech sell Hercules P150 desktop computer for $2400 (includes GST). The owner has kept a record of the number of computers, n, sold per week and the results are shown in this probability distribution (This is a table, but I don't know how to create a table on a thread, I think you will get the idea):

    N............1......2......3.....4
    P(N = n).. 0.1...0.2...0.3...0.4

    The expected sales each week:
    1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4 = 3.

    The calculated variance of the sales each week = 1.

    The fixed costs of the business (salaries, rent, power and so on) are $900 per week and the profit per computer is $375.

    So, the expected profit each week:
    375 (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) - 900 = 225.

    a) Find the variance in profit each week.

    b) Find the standard deviation in profit each week.
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  2. #2
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    If X is a random variable with variance \sigma^2 then the variance of aX+b, for constants a, b is a^2\sigma^2. In your case a=375 and b=-900.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Kiwigirl
    Silica Tech sell Hercules P150 desktop computer for $2400 (includes GST). The owner has kept a record of the number of computers, n, sold per week and the results are shown in this probability distribution (This is a table, but I don't know how to create a table on a thread, I think you will get the idea):

    N............1......2......3.....4
    P(N = n).. 0.1...0.2...0.3...0.4

    The expected sales each week:
    1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4 = 3.

    The calculated variance of the sales each week = 1.

    The fixed costs of the business (salaries, rent, power and so on) are $900 per week and the profit per computer is $375.

    So, the expected profit each week:
    375 (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) - 900 = 225.

    a) Find the variance in profit each week.
    <br />
\mathrm{Var}(prof)=\frac{1}{n}\sum_{i=1}^n (prof_i-\overline{prof})^2\ p(prof_i)<br />
    <br />
=(375-900-225)^2 0.1+(2\times375-900-225)^2 0.2+ (3\times375-900-225)^2 0.3+(4\times375-900-225)^2 0.4<br />

    <br />
=140625<br />

    b) Find the standard deviation in profit each week.
    Standard deviation is the square root of variance and so:

    <br />
\sigma=\sqrt{140625}=\$375<br />

    RonL
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