Question

If the p.d.f. of a continuous random variable X is

f(x) = k (x - x²),    0 < x < 1

= 0,             otherwise

then the value of k is ______.

Options

• 6

• 10

• 12

• 16

Answer 1

If the p.d.f. of a continuous random variable X is

f(x) = k (x - x²),    0 < x < 1

= 0,             otherwise

then the value of k is 6.

Explanation:

Since, f(x) is the p.d.f. of X.

`int_-oo^oo f(x) dx=1`

`=>int_-oo^0f(x)dx+int_0^1f(x)dx+int_1^oof(x)dx=1`

`=>0+int_0^1k(x-x^2)dx+0=1`

`=>k[x^2/2-x^3/3]_0^1=1`

⇒ k = 6