Find the Expected value of the following distributionx -20 -10 30 75 80P(x) 3/20 1/5 1/2 1/10 1/20(a) 20.5(b) 21.5(c) 22.5(d) 24.5
Question
Find the Expected value of the following distribution
| x | -20 | -10 | 30 | 75 | 80 |
|---|---|---|---|---|---|
| P(x) | 3/20 | 1/5 | 1/2 | 1/10 | 1/20 |
(a) 20.5
(b) 21.5
(c) 22.5
(d) 24.5
Solution
The expected value (E) of a probability distribution is calculated by multiplying each outcome (x) by its probability (P(x)), and then summing these products.
So, for the given distribution, the expected value would be calculated as follows:
E = (-20 * 3/20) + (-10 * 1/5) + (30 * 1/2) + (75 * 1/10) + (80 * 1/20)
E = -3 + -2 + 15 + 7.5 + 4
E = 21.5
So, the expected value of the given distribution is 21.5, which corresponds to option (b).
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