APFIVE Variance of a Sum of Independent Variables
An insurance salesperson estimates the daily numbers of auto and home insurance policies sold using independent probability distributions. A student calculates the overall variance in policies sold by averaging the individual variances instead of adding them. What is the mistake in the student’s calculation?
A
Averaging the variances of independent events rather than summing them to get the total variance.
B
Including covariance terms despite the independence of auto and home policies.
C
Converting probabilities into percentages, which led to an incorrect variance calculation.
D
Assuming that the overall standard deviation is the average of the individual standard deviations.
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