a person randomly selects one of six envelopes, each envelope contains a check that the person gets to keep. determine the person's expectation if the six envelope contain checks for $50, $202,$336,$371,$538 $1085 round to the nearest cent as needed

To find the person's expectation, we need to calculate the average amount of money the person can expect to receive.

Let's assign the values of the checks in the envelopes to the variables $$x_1$$ , $$x_2$$ , $$x_3$$ , $$x_4$$ , $$x_5$$ , and $$x_6$$ .

We have:
$$x_1 = 50$$
$$x_2 = 202$$
$$x_3 = 336$$
$$x_4 = 371$$
$$x_5 = 538$$
$$x_6 = 1085$$

The person randomly selects one of the six envelopes. The probability of selecting each envelope is equal since the selection is random. Therefore, the probabilities can be represented as $$\frac{1}{6}$$ for each envelope.

To calculate the expectation, we need to multiply each check value by its probability, and then sum up these products:
$$\text{Expectation} = \frac{1}{6}(50) + \frac{1}{6}(202) + \frac{1}{6}(336) + \frac{1}{6}(371) + \frac{1}{6}(538) + \frac{1}{6}(1085)$$

$$\Rightarrow\text{Expectation}\approx430.33$$

Therefore, the person's expectation is approximately $$430.33.Answer:430.33\boxed{}$$ .