Let X have the uniform distribution U(-1,3). How do you find the p.d.f. of ?

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- Apr 22nd 2009, 02:24 PMlaseruniform distribution / pdf
Let X have the uniform distribution U(-1,3). How do you find the p.d.f. of ?

- Apr 22nd 2009, 02:39 PMmr fantastic
- Apr 23rd 2009, 11:16 PMmatheagle
You need to be careful.

This one to one on 1<x<3 and two to one -1<x<1.

USE .

Now on -1<x<3.

Next notice that y's range is 0 to 9.

WHEN 0<y<1, we have a 2-1 mapping and both

.

So, for 0<y<1, we have

.

But when 1<y<9, we have a 1-1 mapping (with probability one)

So, while .

Thus for 1<y<9, we have

.

AND zero everwhere else.