APFIVE Variance of a Sum of Independent Variables
The numbers of daily auto and home insurance policies sold are modeled by two independent random variables. To find the variance of the total number of policies sold, a student averages the two individual variances. Which of the following best describes the student’s error?
A
Averaging the variances of independent events rather than summing them to get the total variance.
B
Converting probabilities into percentages, which led to an incorrect variance calculation.
C
Including covariance terms despite the independence of auto and home policies.
D
Assuming that the overall standard deviation is the average of the individual standard deviations.
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