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

Grade Probability

A 0.1

B 0.3

C 0.4

D 0.1

F 0.1

1.00

The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a3.0, and so on. Determine the expected grade and variance for the course.