1. (Short questions) Justify all your answers mathematically. (a) For any random variable (\"1, can E [:12] be smaller than E [Ei]2? (b) If 6: and 5 have the same distribution and are independent, is it true that E[Eil~)] = E [21]\"? (c) A teacher of a class of 71 children asks their parents to leave a present under the Christmas tree in the classroom. The day after, each child picks a present at random. What is the expected number of children that end up getting the present bought by their own parents? (Hint: Dene a random variable ii:- that is equal to one when kid 2' gets the present bought by their own parents, and to zero otherwise.)