Exercise: Conditional variance definition

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 ) takes on the value y, then the random variable Var (X" | Y) takes the value E(X - EX|Y = y]) |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 -EXY)] |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