APFIVE Mean of a Transformed Random Variable
A carnival game offers payoffs with the random variable X based on the table shown. The mean of X is $$4$$. If the payoffs are transformed into four new random variables: X, X+4, 3X, and 3X+4, rank these transformations in order of increasing mean value. Express your ordering as an answer with each transformation separated by commas.
| Outcome | Payoff | Probability |
|---|---|---|
| A | $$2$$ | $$0.5$$ |
| B | $$5$$ | $$0.4$$ |
| C | $$10$$ | $$0.1$$ |
A
X, 3X, X+4, 3X+4
B
X+4, X, 3X+4, 3X
C
3X, X, X+4, 3X+4
D
X, X+4, 3X, 3X+4
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