Question

If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by

X = x	- 1.5	-0.5	0.5	1.5	2.5
P(X = x)	0.05	0.2	0.15	0.25	0.35

then, F(1.5) - F(- 0.5) = ?

Options

• 0.2

• 0.4

• 0.1

• 0.3

Answer 1

0.4

Explanation:

Given,

X = x	- 1.5	-0.5	0.5	1.5	2.5
P(X = x)	0.05	0.2	0.15	0.25	0.35

F(X = x) = P(X ≤ x)

∴ F(1.5) = P(X ≤ 1.5)

= P(X = - 1.5) + P(X = - 0.5) + P(X = 0.5) + P(X = 1.5)

= 0.05 + 0.2 + 0.15 + 0.25 = 0.65

F(- 0.5) = P(X ≤ - 0.5)

= P(X = - 1.5) + P(X = - 0.5)

= 0.05 + 0.2 = 0.25

F(1.5) - F(- 0.5) = 0.65 - 0.25 = 0.4