A student was doing a project work, involving a school survey, to find the number of hours spent on study by students, on a randomly selected school day. At the end of the survey he prepared the following report related to the data.

Let x denote the number of hours spent on study by students on a randomly selected school day

then,

$P(X = x) = \begin{cases} 0.2, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } x = 2 \\ k(6-x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}$

where k is unknown constant

Based on the above information answer the Questions