Question: Alice and Bob agree on a positive integer 19. They decide to have children until they either have a girl or they have k: children,

Alice and Bob agree on a positive integer 19. They decide to have children until they either have a girl or they have k: children, Whichever comes rst. Each child is a girl or a boy independently at random with probability 1/2. (a) What is the expected number of girls they Will have? What is the variance? (b) What is the expected number of boys they will have? What is the variance? After having k boys, Alice and Bob decide they really want a daughter and will continue having children until a girl is born. (c) What is the expected number of girls they will have? (d) What is the expected number of boys they Will have? Simplify your answers as much as possible

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