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.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.15
From given information, we find that the probability distribution of X is
|
X |
0 |
1 |
2 |
3 |
4 |
|
P(X) |
0.1 |
k |
2k |
2k |
k |
We know that $Σp_i = 1$
$⇒ 0.1+ k + 2k + 2k + k = 1⇒6k = 1-0.1 = 0.9$
$⇒k=0.15$