Given the probability density functio (p.d.f) of a continuos random variable X as. `f(x)=(x^(2))/(3),-1 lt x lt2`
Determine the cumulative distribution function (c.d.f) X and hence find `P(X lt1),P(X gt0), P(1 lt X lt 2)`.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the Cumulative Distribution Function (C.D.F)

Given the probability density function (p.d.f) of a continuous random variable \(X\) as:

\[
f(x) = \frac{x^2}{3}, \quad -1 < x < 2
...