6. Correct. The answer is false.

a. Let X and Y be the total number of tons produced each day by the two machines. Then:

E(X) = E(Y) = 1(1/6) + 2(1/6) + . . .+ 6(1/6) = 7/2 and

E(X²) = E(Y²) = 1(1/6) + 2²(1/6) + . . .+ 6²(1/6) = 91/6.

Remember that Var[X] = E[X²] - (E[X])². Then, Var (X)=Var(Y) = 91/6 - (7/2)² = 35/12.

Since X and Y are independent, Var(X+Y) = Var (X) + Var(Y) = 35/6.

b. The standard deviation is the square root of the variance Thus: s_X+Y = (35/6)^1/2