# problem with distribution function

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• June 5th 2010, 10:18 AM
noteiler
problem with distribution function
hi there, this problem has really confused me, could someone please help me. the distribution function of random variable A is given, and i must find a distribution function of new random variable B=1/A.
• June 5th 2010, 03:33 PM
matheagle
what is your question?
First of all that distribution function is wrong.
It's ok that F(x)=0 when x is less than 1
and F(x)=1 when x is greater than 2
BUT it cannot be x from 1 to 2.
MAYBE your instructor meant F(x)=x-1, since F cannot exceed 1.
This says that F(1.5)=1.5 which means that $P(X\le 1.5)=1.5$ which is a no-no.

BUT in order to transform, I use calc 1

$f_B(b)=f_A(a)\left|{dA\over dB}\right|$

which can easily be proved by differentiating the cdfs, which was the approach of your teacher.
• June 6th 2010, 01:44 AM
noteiler
Quote:

Originally Posted by matheagle
what is your question?
First of all that distribution function is wrong.

you're right, it was my mistake, i confused it with function which is defined in [0,1], in [1,2] it would be x-1. with this function all stuff works. thanks