Let X denote the number of hours you study on a Sunday. Also it is known that $P(X = x) =\left\{\begin{matrix}0.1&, if\, x = 0\\kx&, if\, x = 1\, or\, 2\\k (5-x)&, if\, x = 3\, or\, 4\\0&,otherwise\end{matrix}\right.$ where k is a constant. Find the value of k.

0.15

The correct answer is Option (3) → 0.15

From given information, we find that the probability distribution of X is

We know that $Σp_i = 1$

$⇒ 0.1+ k + 2k + 2k + k = 1⇒6k = 1-0.1 = 0.9$

$⇒k=0.15$