married couples - geometric distribution


by irony of truth
Tags: couples, distribution, geometric, married
irony of truth
irony of truth is offline
#1
Oct2-04, 10:22 AM
P: 93
A couple plans to continue having children until they have their first girl. Suppose the probability that a child is a girl is 0.5, the outcome of each birth is an independent event, and the birth at which the first girl appears has a geometric distribution. What is the couple's expected family size? Is the geometric pdf a reasonable model?

The expected value of a geometric dist. is 1/p = 1/0.5 = 2.

My problem is the 2nd question: from my point of view.. my answer is yes. Bec. the even only concerns w/ success-girl and failure-boy. Is my reason enough to say that gd. is the reasonable model? =)
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mathman
mathman is offline
#2
Oct2-04, 05:43 PM
Sci Advisor
P: 5,939
The probability that they will have n children (n >=1) is .5n. I presume that is a case of geometric distribution.


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