Thep.d.f of a continous random variable X is
`f(x) = (x^(2))/(3), - 1 lt 1 lt 2`
0 = otherwise
Then the c.d.f of X is

Options

A. `(x^(3))/(9)+(1)/(9)`
B. `(x^(3))/(9)-(1)/(9)`
C. `(x^(2))/(4)+(1)/(4)`
D. `(1)/(9x^(3))+(1)/(9)`

Answer

A

Explanation

Given, `f(x)=(x^(3))/(3)-1lt x lt 2`
0 otherwise
c.d.f. of x is
`F(x)= int_(-1)^(x)f(y)dy`
`=int_(-1)^(x)(y^(2))/(3) dy`
`=1/9[y^(3)]_(-1)^(x)`
`=1/9 (x^(3)+1)`
Hence, correct answer from the given alternatives is (a).