If a curve X has probability density function (pdf)
`f(x)={{:(ax","0lexle1),(a","1lexle2),(3a-ax","2lexle3),(0",""otherewise"):}`
Then, a is equal to

Options

A. 1
B. `1/3`
C. `1/2`
D. `1/5`

Answer

C

Explanation

`therefore f(x)` is a pdf
`therefore" "oversetoounderset(-oo)intf(x)dx=1rArroverset3underset0intf(x)=1`
`rArr" "overset1underset0intf(x)dx+overset2underset1intf(x)dx+overset3underset2intf(x)dx=1`
`rArr" "overset1underset0int(ax)dx+overset2underset1int(a)dx+overset3underset2int(3a-ax)dx=1`
`rArr" "a[x^2/2]_0^1+a[x]_1^2+a[3x-x^2/2]_2^3=1`
`rArr" "a/2+a+a{(9-9/2)-(6-2)}=1`
`therefore" "2a=1`
`rArr" "a=1/2`