Question

The c.d.f. of a discrete r.v. x is 

x	0	1	2	3	4	5
F(x)	0.16	0.41	0.56	0.70	0.91	1.00

Then P(1 < x ≤ 4) = ______ 

Options

• 0.25 

• 0.50

• 0.75

• 0.36

Answer 1

The c.d.f. of a discrete r.v. x is 

x	0	1	2	3	4	5
F(x)	0.16	0.41	0.56	0.70	0.91	1.00

Then P(1 < x ≤ 4) = 0.50.

Explanation:

 P(x = 2) = F(2) - F(1) = 0.56 - 0.41 = 0.15

P(x = 3) = F(3) - F(2) = 0.70 - 0.56 = 0.14

P(x = 4) = F(4) - F(3) = 0.91 - 0.70 = 0.21

∴ P(1 < x ≤ 4) = P(x = 2) + P(x = 3) + P(x = 4)

= 0.15 + 0.14 + 0.21

= 0.50