What is the expected value of the probability distribution of the discrete random variable X?x P(X = x)2 .074 .196 .258 .1110 .0712 .3014 .01
Question
What is the expected value of the probability distribution of the discrete random variable X?
| x | P(X = x) |
|---|---|
| 2 | .074 |
| .196 | .258 |
| 1110 | .0712 |
| .3014 | .01 |
Solution
The expected value (E) of a discrete random variable X is calculated by summing the product of each outcome (x) and its probability (P(X = x)). It is represented as E(X) = Σ [x * P(X = x)].
Given the probability distribution of X:
x P(X = x) 2 .07 4 .196 6 .258 8 .11 10 .07 12 .30 14 .01
We can calculate the expected value as follows:
E(X) = (2 * .07) + (4 * .196) + (6 * .258) + (8 * .11) + (10 * .07) + (12 * .30) + (14 * .01)
E(X) = .14 + .784 + 1.548 + .88 + .7 + 3.6 + .14
E(X) = 7.792
So, the expected value of the probability distribution of the discrete random variable X is 7.792.
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