Financial Risk Manager Part 1
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A motor vehicle production company based in California is assembling its first batch of fully electric cars. After inspecting about 100 newly assembled units, engineers establish that there are a total of 40 defects. While some units have no defects, others have one, two, or more defects. Assume that the distribution of mechanical defects follows a Poisson distribution. Drawing on the first 100 units produced, how many cars, out of every 10,000 units assembled, would we expect to have at least one defect?
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Community
NNikitesh
A
About 330
B
About 0.330
C
About 3,300
D
About 1250
Explanation:
Let's use X to denote the number of defects in a car. X ~ Poi(40/100) i.e. λ = 0.4
P(X is at least 1) = 1 - P(X = 0) = 1 - exp(-0.4) = 0.330
This is the probability of at least 1 defect in a car. Therefore, for every 10,000 cars, we would expect 0.330 * 10,000 = 3,300 units to have one or more defects.
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