Based on the below table, answer the following question:xP(x)30.0540.4050.3060.1570.10What is the expected value?Question 1Answera.4.85b.2.48c.0.3
Question
Based on the below table, answer the following question:xP(x)30.0540.4050.3060.1570.10What is the expected value?Question 1Answera.4.85b.2.48c.0.3
Solution
The expected value (E) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its respective value. It's calculated using the formula:
E(X) = Σ [x * P(x)]
where:
- x is the value of the random variable
- P(x) is the probability of x
Given the table:
| x | P(x) |
|---|---|
| 3 | 0.05 |
| 4 | 0.40 |
| 5 | 0.30 |
| 6 | 0.15 |
| 7 | 0.10 |
We can calculate the expected value as follows:
E(X) = (3 * 0.05) + (4 * 0.40) + (5 * 0.30) + (6 * 0.15) + (7 * 0.10) = 0.15 + 1.60 + 1.50 + 0.90 + 0.70 = 4.85
So, the expected value is 4.85. The correct answer is a. 4.85.
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