# Thread: Function of random variables

1. ## Function of random variables

Dear Everyone,
I have two questions and I will start with the tough one,
Assume I have a random variable y with mean and std Uy and Sy
Now the std of y Sy is equal to:
Sy = F(L) a function of another random variable L
Now the L variable is given as samples (sample readings)
how can I find Sy in terms of SL (given that SL is std for L)
The second question is do you happen to know a good and easy probability and statistics book the cover this issue with applications in engineering?
thank you
sm

2. Originally Posted by sm9999
Dear Everyone,
I have two questions and I will start with the tough one,
Assume I have a random variable y with mean and std Uy and Sy
Now the std of y Sy is equal to:
Sy = F(L) a function of another random variable L
Now the L variable is given as samples (sample readings)
how can I find Sy in terms of SL (given that SL is std for L)
The second question is do you happen to know a good and easy probability and statistics book the cover this issue with applications in engineering?
thank you
sm
I think you need to be more specific about what you want. Can you describe this in terms of a process, say like:

Generate $\displaystyle \sl{l}$ from a distribution $\displaystyle F_L$, then generate $\displaystyle y$from a distribution $\displaystyle F_{Y_{\sl{l}}}$, now we ask what is the standard deviation of $\displaystyle Y$.

CB

3. ## Re: Function of random variables

Thank you CaptainBlack for the reply and sorry for not being clear,
The problem is basically from quantum mechanics, so apologies if the terminology is not correct.
So I have a random variable y represented using a std and mean SDy and Uy.
The random variable y is basically the number of particles in a volume with dimensions L*W*H.
Now SDy was generated using a 3 integrations
SDy = \int \int \int dl.dw.dh which it will generate a formula in terms of L, W, and H.
So far L, W and H are considered constants.
If I want to look at population of volumes (this time) with different L, W, or H, the question would be how SDy can be calculated then? how the new assumption would impact SDy, given that L, W, and H are also represented by mean and stds.
thank you very much
sm