Question

What is the law of large numbers as it relates to calculation of empirical probabilities?

Answer #1

**Solution:**

**Let us understand what theorotical probability and
empirical probability is.**

**Theorotical probability, also known as priori
probability, is the probability of an event before it takes place.
It is calculated by the number of ways the particular event can
occur divided by the total number of possible
outcomes.**

**Empirical probability is the probability of the event
after it has occurred. It is also known as experimental
probability. It is calculated by number of times the event occurs
divided by the total number of incidents observed.**

**Theoretical and empiricall probabilities are linked by
the Law of Large Numbers. This law states that if an experiment is
repeated numerous times, the relative frequency, or experimental
probability, of an outcome will tend to be close to the theoretical
probability of that outcome.**

What is meant by empirical probabilities? Give an
original example. What is meant by classical
probabilities? Give an original example. How do these
differ?

To illustrate the law of large numbers, which we mentioned in
connection with the frequency interpretation of probability,
suppose that among all adults living in a large city w know that
there are as many men as women. Using the normal-curve
approximation, find the probabilities that in a random sample of
adults living in this city the proportion of men will be any where
from 0.49 to 0.51 when the number of persons in the sample is
a) 100; b)...

According to the law of large numbers, what should happen as an
insurance company increases the number of loss exposures that it
insures?
A) Fewer losses should be expected to occur.
B) The amount of premiums needed to cover losses should
decrease.
C) The volatility of the insurance company's underwriting results
should increase.
D) The difference between actual and expected results should
decrease

According to the law of large numbers, what should happen as an
insurance company increases the number of loss exposures that it
insures?
A) Fewer losses should be expected to occur.
B) The amount of premiums needed to cover losses should
decrease.
C) The volatility of the insurance company's underwriting results
should increase.
D) The difference between actual and expected results should
decrease

Apply Chebychev's inequality to prove the Weak Law of Large
Numbers for the sample mean of i.i.d. random variables with a
finite variance.

In plain terms, the Weak Law of Large Numbers states that as the
number of experiments approaches infinity, the difference between
the sample mean and the distribution mean can be as small as
possible.
- TRUE
- FALSE

Select a probability that you rely on all the time that relates
to empirical and subjective probability and explain

According to the law of large numbers, Curran Insurance Group
can ________ by charging each of its policyholders a premium close
to their expected loss as long as they have a large pool of
independent and identical risks.
: break even
B : lose revenue
C : pool risk
D : estimate risk

The weak law of large numbers states that the mean of a sample
is a consistent estimator of the mean of the population. That is,
as we increase the sample size, the mean of the sample converges in
probability to the expected value of the distribution that the data
comes from, provided that expected value is finite. Consider a
numerical example, a Student t distribution with n = 5, the same as
we have already seen earlier in this module....

Explain the substitution effect as it relates to the
demand law

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