Question

The c.d.f. of a discrete r.v. X is

X = x	-4	-2	-1	0	2	4	6	8
F(x)	0.2	0.4	0.55	0.6	0.75	0.80	0.95	1

Then P(X ≤ 4|X > -1) = ?

पर्याय

• `5/9`

• `4/9`

• `1/4`

• `1/5`

Answer 1

`5/9`

Explanation:

P(X = 0) = F(0) - F(-1) = 0.6 - 0.55 = 0.05

P(X = 2) = F(2) - F(0) = 0.75 - 0.6 = 0.15

P(X = 4) = 0.80 - 0.75 = 0.05

P(X = 6) = 0.95 - 0.80 = 0.15

P(X = 8) = 1 - 0.95 = 0.05

P(X ≤ 4|X > -1)

`= ("P"("X" = 0) + "P"("X" = 2) + "P"("X" = 4))/("P"("X" = 0) + "P"("X" = 2) + "P"("X" = 4) + "P"("X" = 6) + "P"("X" = 8))`

`= (0.05 + 0.15 + 0.05)/(0.05 + 0.15 + 0.05 + 0.15 + 0.05)`

`= 0.25/0.45`

`= 5/9`