A random variable X has the following probability distribution
| \(x_i\) | −2 | −1 | 0 | 1 | 2 | 3 |
| \(p_i\) | 0.1 | k | 0.2 | 2k | 0.3 | k |
Then the mean of X is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.8
The probabilities add up to 1:
\(0.1 + k + 0.2 + 2k + 0.3 + k = 1\)
\(0.6 + 4k = 1\)
\(k = 0.1\)
The mean is \(\sum x_i p_i\):
\(\sum x_i p_i = (-2)(0.1) + (-1)(0.1) + 0(0.2) + 1(0.2) + 2(0.3) + 3(0.1)\)
\(= -0.2 - 0.1 + 0 + 0.2 + 0.6 + 0.3 = 0.8\)