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  3. 6. (a). in a particular town 10% of the families h

6. (a). In a particular town 10% of the families have no children, 30% have one child,...

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Basic Math

6. (a).

In a particular town 10% of the families have no children, 30%have one child, 20% have
two children, 40% have three children, and 0% have four. Let Trepresent the total
number of children, and G the number of girls, in a family chosenat random from this
town. Assuming that children are equally likely to be boys orgirls, find the distribution
of G. Display your answer in a table and sketch the histogram.

(b). Find E(T | G=1) = conditional expectation of number ofchildren T, given 1 girl.

(c). Find the sum over k= 0, , 2, 3 of

E (T | G=k) P( G= k).

HINT: The hard way is to compute both factors of all 4 terms anddo the arithmetic. The easy way is to use the R.A.C.E.

Answer & Explanation Solved by verified expert
3.6 Ratings (322 Votes)
a Let T Number of childThe probability mass function of T isT0123PTt010030020040G Number of girls in familyG take values 012 and 3p P A child is a girl 05Since Conditional distribution of G given Tt is    See Answer
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