Timeline for Google question: In a country in which people only want boys
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 12, 2017 at 9:29 | comment | added | KGhatak | @ Gjergji Zaimi : When I try to find out expected number of boy children (Y) for a couple, I was hoping to get $E(Y)=1$, but surprisingly I get $\frac12$. Can you help me understand what's mistake I'm doing. My calculation is: $E(Y)= 0.P(Y=0) + 1.P(Y=1)+ 2.P(Y=2)+.. = 0 + 1. \frac12 + 2.0 + 3.0 + .. = \frac12$ | |
| Jun 29, 2013 at 6:28 | comment | added | David | @GjergjiZaimi. I didn't understand how E(X)=∑n/2^n+1=1. It looks to me the case of arithmetico-geometric series (1/2*0+1/4*1+1/8*2.....) with answer of 2.5 en.wikipedia.org/wiki/Arithmetico-geometric_sequence | |
| May 14, 2013 at 9:37 | comment | added | user112109 | @Douglas Zare: "Showing that E(A)/E(A+B) = 1/2 is not enough. You need another assumption." No, you need nothing else. The original question is: Can the family planning of a set of families result in a set of children such that E(A) differs from E(B)? The answer is no, since probability of 1/2 per girl is a martingale. You have answered another question not relevant in the present context. | |
| Mar 12, 2010 at 11:21 | comment | added | Gjergji Zaimi | Of course I agree, both in the ambiguity of the question and in your argument, which is why I gave you a +1. Your answer is more complete, and I took the lazy man's approach :-) | |
| Mar 12, 2010 at 11:07 | comment | added | Douglas Zare | I guess there is some ambiguity about what number is meant by a proportion A:B. I read it as A/(A+B), which has the nice property that B:A is the complement so that computing E[A:B] is essentially the same as E[B:A]. If you interpret the proportion A:B as A/B, then this may be infinite, and E[A:B] can be 1 while E[B:A] is not 1, and may not exist. This calculation shows E[A/B]=1, but it does not compute E[B/A]. | |
| Mar 12, 2010 at 9:56 | comment | added | zeb | aha! So there are really two questions here: expected proportion of girls to total population and expected proportion of boys to girls. Tricky! | |
| Mar 12, 2010 at 9:49 | comment | added | Gjergji Zaimi | I was finding E(A/B), since B=1 this reduces to E(A). | |
| Mar 12, 2010 at 9:42 | comment | added | Douglas Zare | E[A/(A+B)] is not E(A)/(E(A+B)). Showing that E(A)/E(A+B) = 1/2 is not enough. You need another assumption. | |
| Mar 12, 2010 at 9:14 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |