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Question

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

X31013579
F(x)0.10.30.50.650.750.850.901
Find P(X=3/X<0).

A
0.3333
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B
0.35
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C
0.55
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D
0.25
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Solution

The correct option is A 0.3333
αi f(x) P(X=xi)
3
1
0
1
3
5
7
9
0.1
0.3
0.5
0.65
0.76
0.85
0.90
1
0.1
0.2
0.2
0.15
0.1
0.1
0.05
0.1
P(X=3)=0.1

P(X<0)=P(X=1)+P(X=3)

=0.2+0.1

P(X=3)P(X<0)=0.10.3=0.3333

Hence, the answer is 0.3333.

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