In an experiment on the behavior of young children, each child is placed in an area with five toys. The response of interest is the number of toys that the child plays with. Past experiments with many...

In an experiment on the behavior of young children, each child is placed in an area with five toys. The response of interest is the number of toys that the child plays with. Past experiments with many subjects have shown that the probability distribution of the number of toys played with is as follows:
Number of toys  0        1      2     3
Probability         0.05 0.20 0.44 0.31
Assume we sample a young child at random and let X be the number of toys this child plays with.

Now assume that we independently sample 14 additional children (that gives 15 children total in the sample) and then look only at whether or not  they play with any toys. Let Y be the number of children in our sample who play with at least 1 toy.
(d) What is the distribution of Y and what are the parameters of that distribution?

(e) What are the expected value and the variance of Y ?