Mean of a Transformed Random Variable

Question

The random variable X represents the payoff from a carnival game and has the probability distribution shown in the table. The mean of X is $$4$$. Consider the following four random variables created by transforming X: X, X+4, 3X, and 3X+4. Which of the following correctly orders these random variables by their means, from least to greatest?

| Outcome | Payoff        | Probability |
|---------|---------------|-------------|
| A       | $$2$$         | $$0.5$$     |
| B       | $$5$$         | $$0.4$$     |
| C       | $$10$$        | $$0.1$$     |

Accepted Answer

X, X+4, 3X, 3X+4

Answer

X+4, X, 3X+4, 3X

Answer

X, 3X, X+4, 3X+4

Answer

3X, X, X+4, 3X+4

Outcome	Payoff	Probability
A	$2$	$0.5$
B	$5$	$0.4$
C	$10$	$0.1$

Mean of a Transformed Random Variable

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