Explain why the central limit theory/law of large numbers usually does not work in the real world of most (possibly all) insurance coverages.

Step-by-step explanation:

The law of large numbers stems from the probability theory in statistics. It proposes that when the sample of observations increases, variation around the mean observation declines. In other words, the average value gains predictive power. In the insurance industry, the law of large numbers produces its axiom. As the number of exposure units (policyholders) increases, the probability that the actual loss per exposure unit will equal the expected loss per exposure unit is higher.To put it in economic language, there are returns to scale in insurance production. In practical terms, this means that it is easier to establish the correct premium and thereby reduce risk exposure for the insurer as more policies are issued within a given insurance class . In insurance, with a large number of policyholders, the actual loss per event will equal the expected loss per event. The Law of Large Numbers is less effective in the insurance where policyholders are independent of each other.With the large number of insurers offering different types of coverage, the demand for variety increases, making the Law of Large Numbers less beneficial.

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

7

step-by-step explanation: