Uniform random variable

Hi I have a question about uniform random variable

If X is uniformly distributerd over (a,b) what random variable, having a linear relation with X, is uniformly distributed over (0,1)?

I knew the answer should be very simple, but I don't know how should I proceed. The fact I do know is that the probability density function of the random variable must be
f(x) = { 1 0<x<1
0 otherwise }

But how should I manipulate so that the new random variable would fall into this interval while having a linear relation with X?

One attempt I had was U=(X-a)/(b-a) so that U is in the right interval, but I think U doesn't even have a linear relation to X. So yeah, I'm completely clueless. ]
Thanks.

Quote:

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Originally Posted by ChaosticMoon

One attempt I had was U=(X-a)/(b-a) so that U is in the right interval, but I think U doesn't even have a linear relation to X. So yeah, I'm completely clueless. ]
Thanks.

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But that's a linear relation to X :
which is in the form mx+n

and if you check with the cumulative density function, you'll see that you're not wrong.

Quote:

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Originally Posted by ChaosticMoon

Hi I have a question about uniform random variable

If X is uniformly distributerd over (a,b) what random variable, having a linear relation with X, is uniformly distributed over (0,1)?

I knew the answer should be very simple, but I don't know how should I proceed. The fact I do know is that the probability density function of the random variable must be
f(x) = { 1 0<x<1
0 otherwise }

But how should I manipulate so that the new random variable would fall into this interval while having a linear relation with X?

One attempt I had was U=(X-a)/(b-a) so that U is in the right interval, but I think U doesn't even have a linear relation to X. So yeah, I'm completely clueless. ]
Thanks.

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Consider:



Why is this what you seek, in particular what does it mean to say something has a linear association with X?

CB