If the probability density of a random variable is given by [f(x)= begin{cases}kleft(1-x^{2} ight) & text { for } 0

If the probability density of a random variable is given by

\[f(x)= \begin{cases}k\left(1-x^{2}\right) & \text { for } 0

find the value of \(k\) and the probabilities that a random variable having this probability density will take on a value

(a) between 0.1 and 0.2 ;

(b) greater than 0.5 .

(c) Find \(\mu\) and \(\sigma^{2}\).