Suppose there are 400 possible points to earn in an economics class. For the pur

Question

Suppose there are 400 possible points to earn in an economics class. For the purposes of this problem, we'll assume that there are only 4 possible outcomes. The Distribution Function is given as the following: A) What is the expected value for the score? What is the variance of the score? B) These scores can be also converted into percentages. What is the expected percentage score What is the variance of the percentage score? (We will learn a trick for calculating these quickly in the next section of the class. But for now just use reason.)

Explanation / Answer

Expected value =

250(0.10) + 300 ( 0.30) + 350 (0.35) + 400 (0.25) = 25 + 90 + 122.5 + 100 = 337.5

Variance = E (X2) - [E(X)]2

= [0.10 ( 2502) + 0.30 (300)2 + 0.35 ( 3502 ) + 0.25 (4002) ] - (337.52)

= 2218.75

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