CA Foundation · Quantitative Aptitude · Theoretical Distributions
A shop in Jaipur gets customer complaints at an average of 4 per week, following a Poisson distribution. What is the expected number of complaints in 3 weeks, and its variance?
The mean is 12 and the variance is 12. The weekly rate of 4 scales to 12 over three weeks, and a Poisson distribution always has variance equal to its mean.
- AMean 12, variance 12Correct
- BMean 12, variance 144
- CMean 4, variance 12
- DMean 12, variance 4
Explanation
Over 3 weeks the Poisson parameter scales to 4 * 3 = 12. In a Poisson distribution variance equals mean, so the variance is also 12. Squaring 12 to get 144 wrongly treats variance as the mean squared.
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