Let X1, X2, X3 be a random sample of size 3 from
the distribution with pmf f(x) = 1/4, x = 1,2,3,4.
For example, observe three independent rolls of a fair
four-sided die.
(a) Find the pmf of Y = X₁ + X2 + X3.
(b) Sketch a bar graph of the pmf of Y.