(a) Let X be a random variable having probability density function $$…

Previous year question for Engineering Mathematics-III.

Question

(a) Let X be a random variable having probability density function

$$f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2 - x, & 1 \le x \le 2 \end{cases}$$

Find the mean and variance of X.

(b) The first three moments of a distribution about the value 2 are 1, 6 and 40. Show that the first three moments about zero are 3, 14, 16.