Question

The following is the c.d.f. of r.v. X:

x	−3	−2	−1	0	1	2	3	4
F(X)	0.1	0.3	0.5	0.65	0.75	0.85	0.9	1

P (X ≤ 3/ X > 0)

Answer 1

(X ≤ 3) ∩ (X > 0)

= {−3, −2, −1, 0, 1, 2, 3} ∩ {1, 2, 3, 4}

= {1, 2, 3}

∴ P[(X ≤ 3) ∩ ( X > 0)]

= P(X = 1)+ P(X = 2)+ P(X = 3)

∴ P[(X ≤ 3) / ( X > 0)]

= `(P[(X ≤ 3) ∩ ( X > 0)])/(P(X > 0))`

= `(P(X = 1)  +  P(X = 2)  +  P(X=3))/(P(X = 1) + P(X = 2)  +  P(X = 3) + P(X = 4))`

= `(0.1 + 0.1 + 0.05)/(0.1 + 0.1 + 0.05 + 0.1)`

=`0.25/0.35`

= `5/7`