MHB Distribution of Y: cX+d | X~uniform(0,1)

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When X is uniformly distributed over (0,1) and transformed by Y = cX + d with c < 0, the distribution of Y can be determined. Rearranging the equation gives X = (Y - d) / c, leading to the bounds cL + d < Y < cR + d. Given L = 0 and R = 1, this simplifies to d < Y < c + d. Therefore, Y follows a uniform distribution U(a, b) for specific values of a and b. The transformation effectively shifts and scales the original uniform distribution.
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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?
 
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oyth94 said:
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?
 
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?
 
oyth94 said:
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?

Hi oyth94! :)

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.
 
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