X_2$

Asked May 28 '15 at 07:31

Active May 28 '15 at 07:48

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Find the distribution of $Z = 1/X_1 + 1/X_2$, where $X_1$ and $X_2$ follow normal distribution.

I have $2$ variables with normal distribution, $X_1$ and $X_2$. How can I find the distribution of: $$Z = \frac{1}{X_1} + \frac{1}{X_2}?$$

How can I, then, generalize the method for $n$ variables? $$\left(Z'= \frac{1}{X_1} + \frac{1}{X_2} + \ldots + \frac{1}{X_n}\right)$$

Thanks!

edited May 28 '15 at 07:48

user35603

asked May 28 '15 at 07:31

Lily James

Are $X_1$ and $X_2$ independant ? – Augustin May 28 '15 at 07:36
The question doesn't clarify, but let's assume they are, for simplicity reasons. – Lily James May 28 '15 at 07:41
Did you try to apply the standard procedure? Where were you stuck? – Did May 28 '15 at 08:23
@Did I am not a mathematician, I am a programmer; I need this for a simulation. I would appreciate it if you could tell me how to approach the problem.. – Lily James May 28 '15 at 08:26
Example in action: http://math.stackexchange.com/a/30966/ – Did May 28 '15 at 08:28
If you only need it for simulation, then it is easier to just use a random generator for X1 and X2 and then calculate Z. – wiskundeliefhebber May 28 '15 at 08:39
Thank you. I just would like to know the theoritical result in order to confirm the simulation results afterwards. – Lily James May 28 '15 at 09:14

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