Verify that the following functions are probability mass functions, and determine the requested probabilities.

1.

(a) P(X ‰¤ 2)

(b) P(X > ˆ’2)

(c) P(ˆ’1‰¤ X ‰¤ 1)

(d) P(X ‰¤ ˆ’1 or X = 2)

2. f(x) = (8 / 7) (1 / 2)^x, x = 1,2,3

(a) P(X ‰¤ 1)

(b) P(X > 1)

(c) P(2 < X < 6)

(d) P(X ‰¤ 1 or X > 1)

3. F(x) = 2x + 1/25, x = 0, 1, 2, 3, 4

(a) P(X = 4)

(b) P(X ‰¤ 1)

(c) P(2 ‰¤ X < 4)

(d) P(X > ˆ’10)

4. f (x) = (3 / 4) (1 / 4)^x, x = 0,1,2,€¦

(a) P(X = 2)

(b) P(X ‰¤ 2)

(c) P(X > 2)

(d) P(X ‰¥ 1)

5.

(a) P(X ‰¥ 2)

(b) P(X < 1.65)

(c) P(X = 1.5)

(d) P(X < 1.3 or X > 21)

Transcribed Image Text:

2 -2 -1 0 f(x) 0.2 0.4 0.1 0.2 0.1 0.4 0.1 х 1.25 1.5 1.75 2 2.25 f(x) 0.2 0.4 0.2 0.1 0.1