The following probabilities for grades in management science have been determined based on past records: Grade .....

Question:

The following probabilities for grades in management science have been determined based on past records:
Grade ..... Probability
A ........ 0.10
B ......... 0.30
C .......... 0.40
D ......... 0.10
F ......... 0.10
1.00

The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course.