Married couples - geometric distribution

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SUMMARY

The discussion centers on a couple's decision to have children until they have their first girl, modeled by a geometric distribution with a success probability of 0.5. The expected family size is calculated as 2, derived from the formula for expected value in a geometric distribution, which is 1/p. Participants confirm that the geometric probability distribution function (pdf) is a reasonable model for this scenario, as it accurately represents the independent events of each birth resulting in either a boy or a girl.

PREREQUISITES
  • Understanding of geometric distribution and its properties
  • Knowledge of probability theory, specifically independent events
  • Familiarity with expected value calculations
  • Basic statistics terminology related to probability distributions
NEXT STEPS
  • Study the properties of geometric distributions in-depth
  • Learn about the applications of probability theory in real-world scenarios
  • Explore other probability distributions, such as binomial and Poisson distributions
  • Investigate the concept of expected value in various statistical contexts
USEFUL FOR

Students of statistics, educators teaching probability theory, and anyone interested in understanding family planning through the lens of mathematical modeling.

irony of truth
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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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