If the mean of the probability distribution is 5, then the value of k is:
| X | 2 | k | 5 |
| P(X) | 0.2 | 0.4 | 0.6 |
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
The mean (expected value) of a probability distribution is the sum of each value times its probability:
\(E(X) = \sum x\,P(X = x)\)
With the values in the table and E(X) = 5:
\(2(0.2) + k(0.4) + 5(0.6) = 5\)
\(0.4 + 0.4k + 3 = 5\)
\(0.4k = 1.6\)
\(k = 4\)