4. A newly married couple wants to have children until they obtain children of both sexes.The events of having a boy or girl are independent and equiprobable. Let X be therandom variable that counts the number of children that the couple has until obtainingchildren of both sexes. For example, X (bbbbbbg) = 7 and X(ggggggggb) = 9 whereb stands for 'boy' and g stands for 'girl'. (Note that X is not a negative binomialrandom variable because having a girl or a boy is considered a success. In fact, X isnot one of the standard discrete random variables discussed in class.)(a) Write down the pmf of X, and do not forget to indicate the range of values thatx can take on.px (x) =(b) What is the probability that the couple will have to have at least five children toobtain children of both sexes? Express your answer as a fraction.

Answered: Image /qna-images/answer/a0128e11-4921-4001-b54c-b0a47864a3fc.jpg

Answered: (a) Write down the pmf of X, and do not…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a) Write down the pmf of X, and do not forget to indicate the range of values I can take on. px (x) = (b) What is the probability that the couple will have to have at least five child obtain children of both sexes? Express your answer as a fraction. x =