P(A)=.10, P(B)=.30, P(C)=.40, P(D)=.10, P(F)=.10. Determined the expected grade and variance for the course.
To determine the expected grade for the course, we need to calculate the weighted average of the grades.
First, calculate the product of each grade (A, B, C, D, F) with its corresponding probability:
Grade A: P(A) = 0.10
Grade B: P(B) = 0.30
Grade C: P(C) = 0.40
Grade D: P(D) = 0.10
Grade F: P(F) = 0.10
Expected Grade = (P(A) * A) + (P(B) * B) + (P(C) * C) + (P(D) * D) + (P(F) * F)
Expected Grade = (0.10 * A) + (0.30 * B) + (0.40 * C) + (0.10 * D) + (0.10 * F)
Next, calculate the variance for the course. Variance measures the spread or variability of the grades.
Variance = [(A - Expected Grade)^2 * P(A)] + [(B - Expected Grade)^2 * P(B)] + [(C - Expected Grade)^2 * P(C)] + [(D - Expected Grade)^2 * P(D)] + [(F - Expected Grade)^2 * P(F)]
Variance = [(A - Expected Grade)^2 * 0.10] + [(B - Expected Grade)^2 * 0.30] + [(C - Expected Grade)^2 * 0.40] + [(D - Expected Grade)^2 * 0.10] + [(F - Expected Grade)^2 * 0.10]
Note: The values for A, B, C, D, and F are not given in the question. You will need to substitute the actual grade values into the equations above to obtain the expected grade and variance for the course.