The first part of this question states: Consider a very small town with 50 families with children. Let X be the number of children in a family picked at random from the 50 families with children in the town. Suppose that the family size distribution is given by $ fX(x) = \begin{cases} 0.3 & \text{if } x = 1, \\ 0.4 & \text{if } x = 2, \\ 0.26 & \text{if } x = 3, \\ 0.04 & \text{if } x = 4. \end{cases} $ I then had to calculate the cumulative distribution function and the Expected value and Var(X). I managed to do that all okay. But with the next part of the question I am really stuck: Now suppose that you pick a child at random from the children in this town - each child is equally likely to be picked - and ask the child how many children there are in their family (including the child you asked). Let Y be the size of the child's family. (i) How many children are there in the town?
My thoughts, at first I thought that this might involve me forming a Poisson distribution but they I realised I won't have any parameter to form the distribution with. What distribution would be best to used then? Because it can't be a Bernoulli trial or a Geometric distribution either.