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Forty-four babies—a new record at the time—were born in one 24-hour period at the Mater Mothers’ Hospital in Brisbane, Queensland, on December 18, 1997. There were eighteen girls and twenty-six boys, and the observed mean and standard deviations for birthweights were (in grams)

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Suggest a distribution, including parameter estimates, for each of the following random variables: (a). The time between births; (b). The time between births of boys; (c). The number of births in an hour; (d). The number of girls born between two boys; (e). The number of girls in ten births; (f). The average birthweights for both the boysand the girls.

I don't know what distributions d and f are, and their parameters.

Thank you for your time.

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a). The time between births;

b). The time between births of boys;

c). The number of births in an hour;

d). The number of girls born between two boys;

e). The number of girls in ten births;

f). The average birthweights for both the boysand the girls.

I don't know what distributions d and f are, and their parameters.

For (d), use distribution of the time between births for two boys, and the probability that a count of births for girls will occur within that time.   Let $N_{g;t}$ be the count for girls born within a time interval of length $t$, and $T_b$ be the time interval between the consecutive births of two boys. $$\mathsf P(N_{g;T_b}{=}d)=\int_0^\infty \mathsf p(T_b{=}t)\mathsf P(N_{g;t}{=}d)\mathrm d t$$

For (f), if you may assume the birth weights for each sex follow an approximately Normal Distribution and are independent, then you may use what you know about the sum of independent Normal Distributions.

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