The cumulative probabilities for a distribution.

A probability distribution can also be described by a function that gives the accumulated probability at or below each value of X.

Specifically,

(a) Complete the F (x ) column in this table.

(b) Now cover the f (x ) column with a strip of paper. From the F (x ) values, reconstruct the probability function f (x ).
[Hint: f (x ) F (x ) F (x 1).]

F(c) = = PIX c] f(x) Cumulative distribu- tion function at c = Sum of probabilities of all values x = c * x f(x) F(x) .07 .07 .12 .19 .25 .28 For the probability .18 distribution given 6 .10 here, we calculate 123456 = F(1) PIX1] = f(1) = F(2) P[X2] = f(1) + f(2) = .07 = .19