Question

The p.d.f of c.r.v X is given by f(x) = `("x" + 2)/18`, if −2 < x < 4 = 0, otherwise = 0, then P[|x| < 1] = ____________.

विकल्प

• `2/9`

• `4/9`

• `1/9`

• `1/18`

Answer 1

The p.d.f of c.r.v X is given by f(x) = `("x" + 2)/18`, if −2 < x < 4 = 0, otherwise = 0, then P[|x| < 1] = `underline(2/9)`.

Explanation:

We have, f(x) = `[(("x" + 2)/18, -2 < "x" < 4), (0, "otherwise")]`

P[|x| < 1] = `int_-1^1 (("x" + 2)/18) "dx"`

= `1/18 ["x"^2/2 + 2"x"]_-1^1`

= `1/18 [(1/2 + 2) - (1/2 - 2)]`

= `4/18`

= `2/9`