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If the probability density function of a...

If the probability density function of a random variable X is given as
then F(0) is equal to

A

`P(Xlt0)`

B

`P(Xgt0)`

C

`1-P(Xgt0)`

D

`1-PXlt0)`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that, cumulative distribution function
`F(x)=P(Xlex)`
`therefore" "F(0)=P(Xle0)`
`=P(x=0)+P(x=-1)+P(x=-2)`
`=0.15+0.3+0.2=0.65`
(a) `P(Xlt0)=P(x=-1)+P(x=-2)`
`=0.3+0.2=0.5`
`therefore" "P(Xlt0)neF(0)`
(b) `P(Xgt0)=P(x=1)+P(x=2)`
`0.25+0.1=0.65`
`therefore" "P(Xgt0)neF(0)`
(c ) `1-P(Xgt0)=1-0.35=0.65`
`therefore" "1-P(Xgt0)=F(0)`
Hence, option (c ) is correct
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