A random variable X has the following probability distribution:
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(X) | 0 | m | 2m | 2m | 3m | \(m^2\) | \(2m^2\) | \(7m^2+m\) |
The value of m is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{10}\)
The probabilities add up to 1:
\(0 + m + 2m + 2m + 3m + m^2 + 2m^2 + 7m^2 + m = 1\)
\(10m^2 + 9m - 1 = 0\)
\((10m - 1)(m + 1) = 0\)
So m = 1/10 or m = −1. A probability cannot be negative, and m = −1 would make P(X = 1) = −1, so m = −1 is rejected.
\( \displaystyle m = \frac{1}{10} \)