betterbias

# betterbias - Achieving Better Bias - - - The Better Bias...

This preview shows pages 1–2. Sign up to view the full content.

Sheet1 Page 1 Achieving Better Bias --------- ------ ---- The Better Bias Bureau takes M faced biased dice with known biases and makes from them N faced biased dice with desired biases. More specifically, if you have an M faced biased die with probability pm[j] of throwing face j, for j from 1 though M, but you really want instead an N faced biased die with probability pn[i] of throwing face i, for i from 1 through N, then good old B3 will give you a method of achieving your desires. The method is this. You are to consider throwing your M faced die an infinite number of times and writing out the resulting faces, f1, f2, f3, . .., as an infinite fraction .f1f2f3. .. base M. The fraction will be a number, call it F, in the range from 0 through 1. For any number r, 0 <= r <= 1, we can compute the probabil- ity that F <= r. Let rn[i] be defined so that probability F <= rn[i] = probability that an N faced die throw is k for some k <= i = sum of pn[k] for k from 1 through i Then when you throw a value F with your M faced die, you

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/29/2011 for the course IT 201 taught by Professor K.v.arya during the Spring '11 term at IIT Kanpur.

### Page1 / 3

betterbias - Achieving Better Bias - - - The Better Bias...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online