nhulbert

## thrillcounter.js
const CellTypes= Object.freeze({
  EMPTY: 0,
  RUPOOR: 1,
  BOMB: 2,
});

const SimplifiedCellTypes = Object.freeze({
  EMPTY: 0,
  BAD: 1, // RUPOOR or BOMB
});

## counting_unique_coupons.md

      
        
          
            
              
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                nhulbert
                / counting_unique_coupons.md
            
            
              Last active
              February 12, 2023 03:36
                — forked from bsidhom/counting_unique_coupons.md
            
              
                Compute the distribution of unique (equi-probable) coupons given a fixed number of draws
              
          
        
      
        

      
      
    test Let $a(n,k,p)={n \choose p}{k \brace p}p!$ for which the generating function is $A(x,y,z) = \displaystyle\sum_{n,k,p \geq 1}{a(n,k,p)x^ny^kz^p}$
Suppose that you have a pool of n different types of coupons (one of each) and
want to sample k coupons with replacement. What is the distribution of the
random variable X, which counts the number of distinct coupons observed with
each k-sized sample? I was unable to come up with a closed-form solution on my
own, instead resorting to simulation and brute force. This captures a solution
I was able to find by searching online and putting the pieces together. I've
written the equations below in approximate Wolfram language syntax, since math
typesetting is not available.
	const CellTypes= Object.freeze({
	EMPTY: 0,
	RUPOOR: 1,
	BOMB: 2,
	});

	const SimplifiedCellTypes = Object.freeze({
	EMPTY: 0,
	BAD: 1, // RUPOOR or BOMB
	});