Find the expected value of the random variable a for the following probability…
2025
Find the expected value of the random variable a for the following probability distribution.
a | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
P(a) | 1/15 | 2/15 | 3/15 | 4/15 | 5/15 |
- A.
2.67
- B.
4.71
- C.
5.71
- D.
8.71
Attempted by 545 students.
Show answer & explanation
Correct answer: A
Correct answer: 2.67
For a valid probability distribution, the probabilities must sum to 1. The corrected row is 1/15, 2/15, 3/15, 4/15, 5/15, whose sum is 15/15 = 1.
Now compute:
E(a) = 0*(1/15) + 1*(2/15) + 2*(3/15) + 3*(4/15) + 4*(5/15)
E(a) = (0 + 2 + 6 + 12 + 20)/15 = 40/15 = 8/3 ≈ 2.67
Hence, the expected value is 2.67.