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The following probabilities for grades in management science have been determined based on past records: Grade Probability A 0.1 B 0.2 C 0.4 D 0.2 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.