Question

Suppose the probability that you get an A in any class you take is .3 and the probability that you get a B is .7. To construct a grade point average, an A is worth 4.0 and a B is worth 3.0. a. What is the expected value for your grade point average? b. Would you expect to have this grade point average for each quarter or semester of your school career? Explain.

Answer 1

a) E(X) = 3.30

b) If these are the only two grades (A and B) available in the school, then this calculated expected value will truly be the expected GPA for each quarter or semester But, if like real life, there are other grades available at the school not included in this calculation, then this value seizes to be the expected value for the GPA over any time period.

Explanation:

P(X=xᵢ) = pᵢ

For an A,

P(X=4.0) = 0.3

For a B

P(X=3.0) = 0.7

But E(X) = Σ xᵢpᵢ

E(X) = (0.3 × 4.0) + (0.7 × 3.0) = 3.30

b) If these are the only two grades available in the school, then this calculated expected value will truly be the expected GPA for each quarter or semester But, if like real life, there are other grades available at the school not included in this calculation, then this value seizes to be the expected value for the GPA over any time period.