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.
