Bob (desperately) searching for an N

Bob is noticeably an impaired stupid person, so I have to be (even) more careful.

As I said in see below (after **A**)

Let be N a whole number LESS THAN 13.
If the number of persons is 13 or more, necessarily more than one have at least ONE COINCIDENT BIRTH-MONTH - this is the pigeon principle or Dirichlet´s box theorem (WIKIPEDIA).
_ p(no coincident month match till the month N inclusive) =
= [1 - 1*f(1)/365] * [ 1- 2*f(2)/365] *
*[1 – 3* f(3)/ 365] * …* [1 - (N-1)* f(N-1) / 365]


where
j=1 January , 2 February , 3 Mars , 4 April, …,
11 = November , 12 = December
f(j) = number of days of the j month.
Note that f(2)= 28 + 1/4 (referring to February).

The Readers can see , for example, E. Parsen´s , Modern Probability Theory and Its Applications. Ch.2, Section 2. (Bob: do not try to read it because is too much for you. The examples deals with things as balls and urns and your *spins* infallibly would be disoriented).

Anyway:
I support (with my entire hearth) the Bob´s appeal to find out a qualified referee.
I repeat: *a q-u-a-l-i-f-i-e-d*.


________licas (Luis A. Afonso)


**A**


Date: Mar 12, 2006 8:27 AM
Author: "Luis A. Afonso"
Subject: Bob´s error: not 2 persons Birthday

Bob wrote (thread <birthdays at the same month as a function of N of members>).

*** To change the problem to the same MONTH, for N < 13, (12/12) (11/12) ... ((12-N+1)/12) for all DIFFERENT B-days, and the probability of at least one matching birth-MONTH is 0, 1/12. .23611111, .427083333, .618055555, ..., .999946276829 for N = 1, 2, ..., 12. Or taking any 4 people at random, the probability that you'll have at least two born the same month is .618. ***


My response

Bob in his typically careless way to deal with Probability posted the formula above. He <copied> it from a text-book (formula relative to <the same day>) simply changing the factors from (1 - u/365) to (1 - u/12)
Notably he does not understand (!) why it appears there the quantity u/365 (with u = 1, 2, 365). The formula is WRONG. The correct formula is
: (he could not find a text-book to <copy> it)

___p= product (1 - u* k(u) / 365) being k(u) is number of days the month u:
_______k(1) = 31,…, k(12)=31.

Another thing that the <scrupulous> Bob forget to say is that:
____twins are not allowed
____the rate of births is supposed to be the same whichever the month: any seasonal variation.

What are the consequences to use the formulas? ____CORRECT____for n=12_______p(no matches) = 0.3519816____WRONG____=0.3519956
************
________licas (Luis A. Afonso)
.

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