If \(\mu\) is mean of random variable X, with probability distribution
| x | 0 | 1 | 2 |
| P(X=x) | \(\displaystyle\frac{4}{9}\) | \(\displaystyle\frac{4}{9}\) | \(\displaystyle\frac{1}{9}\) |
then value of \(9\mu + 4\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10
The mean of a random variable is \(\mu = \sum x\,P(X = x)\):
\( \displaystyle \mu = 0 \times \frac{4}{9} + 1 \times \frac{4}{9} + 2 \times \frac{1}{9} \)
\( \displaystyle = \frac{6}{9} = \frac{2}{3} \)
Hence
\( \displaystyle 9\mu + 4 = 9 \times \frac{2}{3} + 4 = 6 + 4 = 10 \)