DiEb
Posts: 241 Joined: May 2008

Quote (Robin @ Oct. 22 2012,02:02)  Got a statistics problem for anyone feeling bored:
(1+mi)*(1+mi+1)*(1+mi+2)*...(1+mn)=(1+X)^n
Suppose each value of M has a standard deviation associated with it. What is the standard deviation of X? Is it a simpler calculation if the standard deviation of each M is the same?
This is from my wife's friend. It's been over 25 years since I've done statistics so I'm rusty and trying to brush up. Any help would be appreciated.
Oh...and the notation is the way it is because I've not figured out how to get series fonts to work. 
Let me clarify:
1) You have a number of random variables M_1 .... M_n and you form the product R= (1+M_1)(1+M_2)...(1+M_n). Those M_i are real valued, independent, and are following an identical distribution.
2) Are asking whether there is a random variable X such that the product R equals (1+X)^n ?
Obviously if n is even and those M are following the Gaussian law then such an X doesn't exist  the right hand side is always positive, while the probability for the left hand to be negative is positive :)
