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SGS
05-04-2005, 03:30 AM
Ok so I am given something is uniformly distributed on the interval (-1,1). Since it's uniform we know the density function for this to be 1/(b-a). I am having a problem getting this into the distribution function. Here is an example. X is uniform on (-1,1) and Y = X^2. I am to find the distribution function for this. I get f(x)=(1/2)x. The book says f(x)=(1/2)x+(1/2). Where does this (1/2) come from. Thanks in advance.

SGS

pzhon
05-04-2005, 03:51 AM
There must be an error somewhere. As a check, the total probability is 1.

Let f(x) be the density of X at x. To find the density of g(X) at y, add up f(x)/|g'(x)| for each x so that g(x)=y.

Here, f(x)=1/2 for -1&lt;x&lt;1, and g(x)=x^2. For 0&lt;y&lt;1, you get two terms, one for x=-sqrt(y) and one for x=+sqrt(y).

SGS
05-04-2005, 04:18 AM
Problem is there is another example that I get a different distribution function for too. In this one X is uniform on (-pie/2,pie/2). Y=tan x. I get F(x)=pie/2, the example says F(x)=pie/2+(1/2). I have no idea where this half is continually coming from. What do you get as the distribution function for x?

SGS

SGS
05-04-2005, 04:22 AM
Nevermind I have it figured out. Thanks

SGS