Find k, if the following is p.d.f or r.v.f X.
`f(x) = {{:(kx^(2)(1-x), 0 lt x lt 1),(0, "otherwise"):}`

Explanation

To find the value of \( k \) such that the given function \( f(x) \) is a probability density function (PDF), we need to ensure that the integral of \( f(x) \) over its entire range equals 1.

Given:
\[
f(x) =
\begin{cases}
kx^2(1-x) & \text{for } 0 < x < 1 \\
0 & \text{otherwise}
...