$\"\"$

\

The function $\"\"$ .

\

(a)

\

Find the value of $\"\"$ .

\

$\"\"$ is a probability density function.

\

If $\"\"$ is a probability density function then it must satisfy $\"\"$ .

\

Therefore, $\"\"$

\

$\"\"$

\

Apply the formula: $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(b)

\

Find $\"\"$ .

\

The probability that $\"\"$ lies between $\"\"$ and $\"\"$ is $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ $\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) $\"\"$ .