The discussion revolves around verifying calculations related to probability density functions (PDF), cumulative distribution functions (CDF), and their inverses. The original poster presents a piecewise-defined PDF and seeks confirmation of their derived CDF and inverse CDF.
The discussion is ongoing, with participants actively engaging in identifying potential errors in the original poster's calculations. There is a recognition of the need to reassess the chosen root for the inverse CDF, but no consensus has been reached yet.
Participants are considering the implications of the chosen root on the validity of the inverse CDF, particularly regarding its range and adherence to the properties of cumulative distribution functions.
You chose the wrong root for ##.5 \leq x \leq 1##. Can you see why?zzmanzz said:Homework Statement
I was hoping someone could just verify this solution is accurate.
p(x) =
0 , x < 0
4x, x < .5
-4x + 4 , .5 <= x < 1
Find CDF and Inverse of the CDF.
Homework Equations
The Attempt at a Solution
CDF =
0 , x < 0
2x^2 , 0 <= x < .5
-2x^2 + 4x - 1 , .5 <= x <= 1
1, x > 1
Inverse of the CDF
0 , x < 0
sqrt( x / 2) , 0 <= x < .5
1 + sqrt ( 1 - x) / sqrt ( 2 ) , .5 <= x <= 1
1, x > 1
Thanks[/B]
Ray Vickson said:You chose the wrong root for ##.5 \leq x \leq 1##. Can you see why?
zzmanzz said:Thanks for pointing that out. The value for that should also be between .5 and 1, and with that root, it can be greater than 1?
Thank you!Ray Vickson said:Yes, just look at it: you have ##1 + \text{something positive}##.