Married couples - geometric distribution

AI Thread Summary
The couple's expected family size when having children until their first girl is calculated using the geometric distribution, yielding an expected value of 2. Each birth is an independent event with a 50% probability of being a girl. The discussion confirms that the geometric probability density function (pdf) is a reasonable model for this scenario, as it effectively captures the success-failure nature of the births. The probability of having n children before the first girl is indeed represented by the geometric distribution formula. Overall, the geometric model appropriately applies to this couple's situation.
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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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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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