Q.52 The probability distribution for a discrete random variable X is given below.
| X | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| P(X) | 0.3 | 0.4 | 0.2 | 0.1 |
The expectation value of X is (up to one decimal place) ________
How to Calculate the Expected Value of a Discrete Random Variable – Solved Example
Given Probability Distribution:
| X | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| P(X) | 0.3 | 0.4 | 0.2 | 0.1 |
Formula for Expected Value
E(X) = Σ [X × P(X)]
Step-by-Step Calculation
- 1 × 0.3 = 0.3
- 2 × 0.4 = 0.8
- 3 × 0.2 = 0.6
- 4 × 0.1 = 0.4
Total: 0.3 + 0.8 + 0.6 + 0.4 = 2.1
Final Answer
The expectation value of X = 2.1 (correct to one decimal place)
