1. This part is True or False:

Every person has a random number of children, drawn from a common distribution with mean 3 and variance 2. The numbers of children of each person are independent. Let My be the number of grandchildren of a certain person. Then: E [M = Var (M) =A class consists of three sections with 10 students each. The mean quiz scores in each section were 40, 50, 60, respectively. We pick a student, uniformly at random. Let X be the score of the selected student, and let ) be the number of his/her section. The quantity Var (X | Y = y) tumed out to be equal to 5y for each section (y = 1, 2, 3). (a) The random variable E [X Y] has: 3 mean of: a variance of: (b) E Var (X | Y)] = (c) Var (X) =For each one of the following statements, indicate whether it is true or false. (a) if X" = Y (i.e., the two random variables always take the same values), then Var (X | Y) = 0. Select an option v (b) If X = Y (the two random variables always take the same values), then Var (X | Y) = Var (X). Select an option v (c) If Y takes on the value y, then the random variable Var (X | Y") takes the value E(X - EXY=]) |Y=y]. Select an option v (d) If Y takes on the value y, then the random variable Var (X | Y") takes the value E (X -EX|Y) |Y=y] Select an option v (e) If Y takes on the value y, then the random variable Var (X | Y") takes the value E[(X - E[X]) |Y = y.] Select an option v