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Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani
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From families with three children a family is chosen at

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QUESTION:

From families with three children a family is chosen at random. Let X be the number of girls in the family. Calculate and sketch the distribution function of X. Assume that in a three-child family all gender distributions are equally probable.

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QUESTION:

From families with three children a family is chosen at random. Let X be the number of girls in the family. Calculate and sketch the distribution function of X. Assume that in a three-child family all gender distributions are equally probable.

ANSWER:

Step 1 of 3

Given information:

A family is chosen at random from families with three children. Assume that in a three-child family all gender distributions are equally probable.

Let X be the number of girls in the family.

It is required to calculate and sketch the distribution function of X.

The number of children in the family are 3 and the probability of girls in the family are to be obtained.

Here X follows binomial distribution as the probability of having a girl is same as that of the probability of having a boy which is equal to .

Therefore, probability mass function of x is given as:

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