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Let X is a continuous random variable wi...

Let X is a continuous random variable with probability density function
`f(x)={{:(x/6+k,0lexle3),(0," otherwise"):}`
The value of k is equal to

A

`1/(12)`

B

`1/3`

C

`1/4`

D

`1/6`

Text Solution

Verified by Experts

The correct Answer is:
A
`oversetoounderset(-oo)intf(x)dx=1rArr0+overset3underset0int(x/6+k)dx+0=1`
`rArr" "[x^2/(12)+kx]_0^3=1rArr3/4+3k=1`
`rArr" "3k=1/4rArrk=1/(12)`
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