# Thread: the standard deviation of Z=X/Y

1. ## 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 couldnt find any relationship between the standard deviation of Z, X and Y.

how can i approximate Z to normal random variable?

thanks!

2. 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 dont know what this assumtion is needed or not. but...i thought it is better to tell everything about my assumtions.

anyway thx!

3. Originally Posted by Melren
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?

4. Originally Posted by mr fantastic
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!