Chapter 10.1, Problem 27E

(a)

To determine

The probability $P\left(\frac{1}{2}\le X\le 1\right)$, such that the probability density function is $f\left(x\right)$ which is defined on the interval $\left[0,2\right]$.

(b)

To determine

The probability $P\left(\frac{1}{2}\le X\le \frac{3}{2}\right)$, such that the probability density function is $f\left(x\right)$ which is defined on the interval $\left[0,2\right]$.

(c)

To determine

The probability $P\left(X\ge 1\right)$, such that the probability density function is $f\left(x\right)$ which is defined on the interval $\left[0,2\right]$.

(d)

To determine

The probability $P\left(X\le \frac{3}{2}\right)$, such that the probability density function is $f\left(x\right)$ which is defined on the interval $\left[0,2\right]$.