In an experiment on the behavior of young children, each subject is placed in an area with five toys. The variable of interest X is the number of toys that the child plays with. Past experiments with many subjects
have shown that the probability distribution of the number X of toys played with is as follows:
X (number of toys) 0 1 2 3 4 5
P (X) 0.03 0.16 0.30 0.23 0.17 0.11

a) How many toys might you expect a child to play with?
b) What is the standard deviation of the number of toys played with?
c) Describe how you might carry out a simulation to estimate the mean number of toys played with
(don't actually do the simulation, just set it up).