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Math Help - the standard deviation of Z=X/Y

  1. #1
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    the standard deviation of Z=X/Y

    Hello everyone

    if X and Y are independent, positive-valued random variable which are following normal distribution and let Z be their quotient Z=X/Y,

    then i want to approximate Z to normal random variable.

    When I calculated the mean and standard deviation of Z using MATLAB, the mean of Z is similar to (mean of X)/(mean of Y). however i couldn`t find any relationship between the standard deviation of Z, X and Y.

    how can i approximate Z to normal random variable?

    thanks!
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  2. #2
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    ah. i forgot to tell another assumtion.

    the standard deviation values of X and Y are 1%~20% of their mean values.

    when the standard deviation value is bigger than that, the difference between the mean value of Z and (mean of X)/(mean of Y) become larger.
    i don`t know what this assumtion is needed or not. but...i thought it is better to tell everything about my assumtions.

    anyway thx!
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  3. #3
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    Quote Originally Posted by Melren View Post
    Hello everyone

    if X and Y are independent, positive-valued random variable which are following normal distribution [snip]
    How can they be positive-valued and also follow a normal distribution?
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    How can they be positive-valued and also follow a normal distribution?
    hm.... In my problem, the mean value of X and Y are larger than 0 and the standard deviation value are 10% of their mean value. so i thought X and Y can be positive-valued and follow a normal distribution.

    for example, if we assume Y is the thickness of silicon oxide and X is the voltage beween silicon oxide, then Z(=X/Y) is the electric field of silicon oxide. And X and Y are generally assumed to a normal distribution.

    actually, the voltage between silicon oxide (X) can be negative-valued. but i ignored that case for simplicity.

    hmm is this enough explanation? there can be wrong assumtions..

    anyway thx!
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