Question

The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x²). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.

Options

• 3

• `1/3`

• 1

• `1/6`

Answer 1

The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x²). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is 3.

Explanation:

We have, f(x) = `{(3(1 - 2x^2)"," 0 < x < 1),(0 ","   "otherwise"):}`

F(X = n) = P(X ≤ x) = `int_0^x "f"(x)` dx

`= int_0^x 3(1 - 2x^2)`dx

`= [3 (x - "2x"^3/3)]_0^x`

`= 3(x - "2x"^3/3)`

∴ k = 3