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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

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#### Solution

`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`.

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