Change of variable (Continuous rv)

[tta16]

Hello everyone, i was wondering if i'm doing the transformation of continuous rv correctly using the cdf method. It looks correct to me but i dont have the variable d like the question tells me to prove.

Let X ∼ Uniform[L, R]. Let Y = cX + d, where c > 0. Prove that Y ∼ Uniform[cL + d, cR + d].

 

[tkhunny]

1) Can you do it without the calculus? It's just rectangles.
2) Have you been introduced to "Moments"?
3) Is L > 0?

 

[tta16]

1) Can you do it without the calculus? It's just rectangles.
2) Have you been introduced to "Moments"?
3) Is L > 0?

No i dont think so and I haven't been introduced to "Moments" and yeah c>0, nothing about L and R.

I'm using this text book and we are currently on chapter 2.6, the textbook uses another formula other than the cdf method and i was just curious if i applied it correctly. http://www.utstat.toronto.edu/mikevans/jeffrosenthal/


Thanks in advance!

 

[tkhunny]

How did you select zero (0) as the lower bound of your integrals?