Married couples - geometric distribution

In summary, the couple plans to have children until they have their first girl, with a probability of 0.5 for each child being a girl. The expected family size can be calculated using the geometric distribution, with an expected value of 2. The question of whether the geometric distribution is a reasonable model is subjective, but it can be argued that since the only outcomes of interest are success (having a girl) and failure (having a boy), the geometric distribution is a reasonable model for this situation.
  • #1
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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  • #2
The probability that they will have n children (n >=1) is .5n. I presume that is a case of geometric distribution.
 
  • #3


Yes, your reasoning is correct. Since the probability of having a girl is constant and each birth is independent, the geometric distribution is a reasonable model for the couple's family size. The expected value of 2 means that on average, the couple will have 2 children before having their first girl. However, it is important to note that this is just an average and the actual number of children could be more or less than 2.
 

What is the geometric distribution?

The geometric distribution is a probability distribution that models the number of trials needed to achieve the first success in a series of independent trials with a constant probability of success. In the context of married couples, it can be used to model the number of attempts needed to have a successful marriage.

How is the geometric distribution used to study married couples?

In the study of married couples, the geometric distribution can be used to determine the probability of a successful marriage based on the number of attempts or marriages. It can also be used to analyze the timing of marriage or divorce in a population.

What are the assumptions of the geometric distribution in the context of married couples?

The assumptions of the geometric distribution in the context of married couples include that each marriage attempt is independent and has a constant probability of success. It also assumes that the probability of success in one marriage attempt does not affect the probability of success in subsequent attempts.

How can the geometric distribution be applied to real-life situations involving married couples?

The geometric distribution can be applied to real-life situations involving married couples by using it to analyze the success rate of marriages in a specific population. For example, it can be used to determine the average number of marriages a person has before finding a successful marriage, or the probability of a marriage lasting a certain number of years.

Are there any limitations to using the geometric distribution in studying married couples?

Yes, there are limitations to using the geometric distribution in studying married couples. It assumes that each marriage attempt has the same probability of success, which may not always be the case in real-life situations. It also does not account for external factors that may affect the success of a marriage, such as cultural or societal norms.

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