Can expected value be infinite?

It is not surprising that the expected value is infinite when infinity is a possible value. However, the expected value can be infinite, even if the random variable is finite-valued. Let’s look at an example.

Why does the law of large numbers hold?

The law of large numbers, in probability and statistics, states that as a sample size grows, its mean gets closer to the average of the whole population. In a financial context, the law of large numbers indicates that a large entity which is growing rapidly cannot maintain that growth pace forever.

What are the assumptions we need for the weak law of large numbers?

The Weak Law of Large Numbers, also known as Bernoulli’s theorem, states that if you have a sample of independent and identically distributed random variables, as the sample size grows larger, the sample mean will tend toward the population mean.

Is it possible for a random variable to have infinite mean?

Not possible. A distribution with finite mean and infinite variance.

Can a random variable be infinite?

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile. A continuous random variable is not defined at specific values.

What is the effect of large numbers and average on prediction?

The Law of Large Numbers According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

What is the difference between weak law of large numbers and strong law of large numbers?

The weak law of large numbers refers to convergence in probability, whereas the strong law of large numbers refers to almost sure convergence. We say that a sequence of random variables {Yn}∞n=1 converges in probability to a random variable Y if, for all ϵ>0, limnP(|Yn−Y|>ϵ)=0.

Does law of large numbers require finite variance?

Results like this are called a “law of large numbers.” Note that the above random variable has mean zero and variance one. There are better versions of the theorem in the sense that they have weaker hypotheses (you don’t need to assume the variance is finite).