2.1-3. For each of the following, determine the constant
c so that f (x) satisfies the conditions of being a pmf for
a random variable X, and then depict each pmf as a line
graph:
(a) f (x) = x/c, x = 1, 2, 3, 4.
(b) f (x) = cx, x = 1, 2, 3, . . . , 10.
(c) f (x) = c(1/4)x, x = 1, 2, 3, . . . .
(d) f (x) = c(x + 1)2, x = 0, 1, 2, 3.
(e) f (x) = x/c, x = 1, 2, 3, . . . , n.
(f) f (x) = c
(x + 1)(x + 2)
, x = 0, 1, 2, 3, . . . .
Hint: In part ( f ), write f (x) = 1/(x + 1) − 1/(x + 2).