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- Thread starter oyth94
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- Jan 17, 2013

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Let X~ uniform(0,1), ie f(x) = 1/(R-L) for L<x<R and c<0. Let Y= cX+d. What is the distribution of Y?

Think about what happen to X when you add d.

Or

Try to think about what would happen if you only have c*X

What would happen if d was equal to 1?

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- Mar 5, 2012

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Hi oyth94!I rearranged Y=cX+d to get X=(Y-d)/c and substitute it into L<x<R

So it's L< (Y-d)/c < R => cL + d < Y< cR+d

So is that the dist. of Y?

Yes, that is the case.

Btw, you can make your result a little more specific.

Note that your X distribution is U(0,1).

Those 0 and 1 mean that your L=0 and your R=1....

It also means that you can write Y ~ U(a,b) for some a and b.