A random variable X has the probability function \(P(X=x)=\begin{cases}k; & \text{if } x=0\\ 3k; & \text{if } x=1\\ 5k; & \text{if } x=2\end{cases}\), where k is a constant. Then the value of k is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{9}\)
The probabilities add up to 1:
\(k+3k+5k = 1\)
\(9k = 1\)
\( \displaystyle k = \frac{1}{9} \)