# hakank / gist:944856 Created April 27, 2011

### SSH clone URL

You can clone with HTTPS or SSH.

Birthday Paradox ("Surprise") in K (Kona)

View gist:944856
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 ```/ This is a simulation of the "Birthday paradox" / (what I call "Birthday surprise") / See http://en.wikipedia.org/wiki/Birthday_problem   / Take 20 samples of 0..364 with replacement / This represents the birthday of 20 persons. 20 ? 365   / sample result / 195 361 24 274 145 108 157 259 51 228 330 88 180 228 86 197 121 182 336 133   / count how many unique values there are / ? here means the unique values of a vector / # here means the size #?20?365 / sample result: 19   / check how many non unique values there are {20-(#?20 ? 365)} / sample result: 1   / Now run this 10 times. / The phrase / {...}' !10 / means that we run the function in {} / 10 times (for 0..9) {20-(#?20 ? 365)}' !10   / sample result: / 0 0 1 0 0 0 1 1 0 0   / Here we check how many times / there is at least one double (triple, etc), / and run for 10000 simulations.   / 20 person {+/x % #x}({(20-(#?20 ? 365))>0}' !10000) / sample result: 0.4147   / 23 persons {+/x % #x}({(23-(#?23 ? 365))>0}' !10000) / sample result: 0.5093     / Later comment: / Scott Vokes (silentbicycle) suggested this more / direct approach (at twitter) / """ / About your birthday surprise K pg., you can also say / 10 f/init / for "run f 10x, starting w/ init" / or / 10 f\init / to save intermed. vals / """ / Here's a simulation for 20 people and 1000 trials bsup:{~x=#?x?365} par:{(+/x {bsup[20]}\1)%x} par[1000]     ```