Unformatted text preview: is.
is. The Birthday Paradox In a room with n people, what is the probability that we will
In
find at least 2 people who have the same birthday (there
are m = 365 possible choices of birthday)?
An approximate analysis:
An approximate Assuming birthdays are uniformly distributed over the
Assuming
entire year. For any given pair of people, the possibly of
them having the same birthday is 1/m = 1/365 ;
them There are nC2 = n(n1)/ 2 ways to select a pair out of n
There
people
people Let Pcollision be the Probability of at least one collision,
P
collision approx. = n(n1)/2 * 1/m = n(n1)/2m ; Pcollision > ½ when n >= 20 In general, Pcollision > ½ when n becomes >= √ m
In The approximation is not good when n approaches m Where is the approximation ? The Birthday Paradox (cont’d) In a room with n people, what is the probability that we will
In
find at least 2 people who have the same birthday (there
are m = 365 possible choices of birthday)?
365
An exact analysis:
An exact Assuming birthdays are uniformly distributed over the
Assuming
e...
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This note was uploaded on 12/05/2013 for the course IERG 4130 taught by Professor Chowszeming,sherman during the Fall '13 term at CUHK.
 Fall '13
 CHOWSzeMing,Sherman

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