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Thread: Variance of two deterministic distributions

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    Variance of two deterministic distributions




    I would like to know the variance of two deterministic distributions when putting them together.

    Of course the variance of the two seperate deterministic distributions is zero, right?

    I have a machine that processes products and with chance x it processes product A and with chance 1-x it processes product B, so the chances are known.

    What will be the variance of the processing time of the machine?

    Thank you in advance!

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    Re: Variance of two deterministic distributions

    http://en.wikipedia.org/wiki/Varianc...andom_variable

    In particular you may take a look at the Bernoulli distribution which take values \{0, 1\}:

    http://en.wikipedia.org/wiki/Bernoulli_distribution

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    Re: Variance of two deterministic distributions

    Quote Originally Posted by BGM View Post
    http://en.wikipedia.org/wiki/Varianc...andom_variable

    In particular you may take a look at the Bernoulli distribution which take values \{0, 1\}:

    http://en.wikipedia.org/wiki/Bernoulli_distribution
    Thank you I understand it.

    My p will be then r/(r+r/t), I can fill that in in the formula for the variance p(1-p). But, in the bernoulli distribution, the values are 0 or 1 and in my assignment this is between different numbers, and I think that these numbers influence the variance. Is that true? So, do I have to convert the variance formula with my other values? And so, how?

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    Re: Variance of two deterministic distributions

    Let say you have a discrete random variable X with only 2 support points \{a, b\}

    And you correctly obtain that \Pr\{X = a\} = p = 1 - \Pr\{X = b\}.

    So you look at the formula I posted before. To use it you need to calculate

    E[X] = pa + (1 - p)b first.

    Then use either version of it will do.

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    Re: Variance of two deterministic distributions


    Quote Originally Posted by BGM View Post
    Let say you have a discrete random variable X with only 2 support points \{a, b\}

    And you correctly obtain that \Pr\{X = a\} = p = 1 - \Pr\{X = b\}.

    So you look at the formula I posted before. To use it you need to calculate

    E[X] = pa + (1 - p)b first.

    Then use either version of it will do.
    OK, I have now calculated E [X] andE [X] ^2. And then variance = E [X] ^2 - E [X].
    Now I need de covariation coefficient. I wonder if it is simply my E [X]/variance, or something else because it is a discrete distribution?

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