Question

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 0 when X = 1 and Y = 1 when X = 0. What is the mean and variance of X + Y?

Answer 1

If $X=0,$ then $X+Y=0+1=1.$

If $X=1,$ then $X+Y=1+0=1.$

Then $P(X+Y=1)=1.$

$$mean=E(X+Y)=1$$

$$Var(X+Y)=E((X+Y)^2)-(E(X+Y))^2=0$$