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Expected Value of a Random Variable

EMETRC-EXGTWO

Suppose a student's parents offer them a bonus based on their GPA, such that:

$$BONUS = 100 + 10GPA^{2}$$

What is the expected value of the bonus if GPA can take on the whole values of $(0, 1, 2, 3, 4)$ with respective probabilities of $(1/10, 1/10, 2/5, 3/10, 1/10)$?

A

$3$

B

$100$

C

$190$

D

$220$

E

$310$