Question

The following function represents the p.d.f of a.r.v. X

f(x) = `{{:((kx;, "for"  0 < x < 2, "then the value of K is ")),((0;,  "otherwise")):}` ______ 

Options

• `3/2`

• `1/2`

• 1

• 0

Answer 1

`bb(1/2)`

Explanation:

f(x) is a p.d.f of random variable x.

∴ `int_a^b f(x).dx` = 1

⇒ `int_0^2 kx.dx` = 1

⇒ `k[x^2/2]_0^2` = 1

⇒ `k(2^2/2 - 0)` = 1

⇒ 2k = 1

⇒ k = `1/2`.