Probability Q: [e - h / 100]/[e - h], e = 2^52, h randomly between 0 & e - 1

[Holderbert]

Hey there,

So i have been working on this problem but i can't seem to figure it out.

[FONT=&quot]e - h/100[/FONT]
[FONT=&quot] ---------[/FONT]
[FONT=&quot] e - h

[/FONT]e is a big number, but it doesn't really matter what it is (it's 2^52)
h is a random number between 0 and e-1 inclusive

A.) What i want is if h is halfway through its range(h*0.5) the outcome to be 2 but instead it gives me (e-h*0.5/100)/(e-0.5*h)=1.99. Same goes for h if its 1/4 thorugh its range for example. I get 1.33 when i want it to be1+1/3.
It basically goes from being 0 off when h is at its minimum 0 to being 1% off when h is at its maximum.
What would i have to change on the formula above for it not to be off by a factor from 0-1%?

B.)What would i have to do to get a formula which is always 2% off and doesn't scale like the one 1 have?

E.g. In this case i'd want the result to be 1.96 for h*0.5 and 1.306667 for h*0.25


Feel free to ask me if something is unclear.


Holderbert

 

[Holderbert]

Scaling Problem

[FONT=Roboto, arial, sans-serif]I am trying to achieve a consistent reduction by 4% of the outcome using this formula

1/(1-h/e)
[/FONT]e is a big number, but it doesn't really matter what it is (it's 2^52)
h is a random number between 0 and e-1 inclusive

Is there any way i can a reduction by 4% even though ill still get 1 as a result for h=0. So just taking everything times 0.96 wont work.


Holderbert