Question

The pdf of a random variable X is

f(x) = 3(1 - 2x²), 0 < x < 1

      = 0   otherwise

The P`(1/4 < "X" < 1/3)` = ?

Options

• `179/864`

• `159/864`

• `169/864`

• `189/864`

Answer 1

`179/864`

Explanation:

We have, p.d.f of a random variable

X is f(x) = 3(1- 2x²), 0 < x < 1

= 0, otherwise

`therefore "P"(1/4 < "X" < 1/3) = int_(1//4)^(1//3)`f(x) dx

= `int_(1//4)^(1//3) 3(1 - 2x^2) "dx"`

`= 3 [x - 2/3 x^3]_(1//4)^(1//3)`

`= 3[(1/3 - 2/3 (1/3)^3) - (1/4 - 2/3(1/4)^3)]`

`= 3[(1/3 - 1/4) - 2/3(1/3^3 - 1/4^3)]`

`= 3[1/12 - 2/3 xx 37/1728]`

`= 3 xx 179/2592`

`= 179/864`