The Poisson distribution.
The significance of the mean of a probability distribution is that it is the most probably thing to happen. The mean is the average of a set of values. If it is the average of a probability distribution, it is the most probable part.
The expected value is the average of a probability distribution. It is the value that can be expected to occur on the average, in the long run.
Because, whatever the underlying distribution, as more and more samples are taken from ANY population, the average of those samples will have a standard normal distribution whose mean will be their average. The normal (or Gaussian) distribution is symmetric and so its mean lies at the centre of the probability distribution.
Variance
The central limit theorem is one of two fundamental theories of probability. It's very important because its the reason a great number of statistical procedures work. The theorem states the distribution of an average has the tendency to be normal, even when it turns out that the distribution from which the average is calculated is definitely non-normal.
It is a theoretical probability distribution. I have included two links from the internet which describe the distribution and some of its applications. Sometimes in statistics, we are more interested in the more extreme statistics rather than the average. For example, if we are studying the spread of a disease, perhaps the long distance that the disease can travel one time in 100 is more important than the average distance. Both the exponential and the Pareto distribution are used when the tail end probabilities (cumulative probability close to 1) are of interest. See related links.
Following are some applications:- 1)Computing grades from test scores by using the bell curve to find the average. 2)Same applies to any other normally distrubuted quantity like height,weight etc. • The normal distribution is a distribution that is centered around an average value with an even spread in both directions (standard deviation). • This makes the distribution symmetrical! • This symmetry causes the mean, median, and mode to be the exact same value. • Symmetry will come in handy when calculating probabilities.
The mean of a distribution of scores is the average.
Mean means Average of a particular distribution Mean means Average of a particular distribution
The average of all the naturally occurring isotopes of a particular element are an element's atomic Mass.
I have no idea what you mean by inducing a distribution.If you assume that the number of events - people joining the queue - in a given time interval has a constant average rate and the the events are independent of one another, then arrivals in the queue follow a Poisson distribution.
The significance of the mean of a probability distribution is that it is the most probably thing to happen. The mean is the average of a set of values. If it is the average of a probability distribution, it is the most probable part.
The expected value is the average of a probability distribution. It is the value that can be expected to occur on the average, in the long run.
Because, whatever the underlying distribution, as more and more samples are taken from ANY population, the average of those samples will have a standard normal distribution whose mean will be their average. The normal (or Gaussian) distribution is symmetric and so its mean lies at the centre of the probability distribution.
1,123,846,763,559
When studying the sum (or average) of a large number of independent variables. A large number is necessary for the Central Limit Theorem to kick in - unless the variables themselves were normally distributed. Independence is critical. If they are not, normality may not be assumed.
The standard deviation of a distribution is the average spread from the mean (average). If I told you I had a distribution of data with average 10000 and standard deviation 10, you'd know that most of the data is close to the middle. If I told you I had a distrubtion of data with average 10000 and standard deviation 3000, you'd know that the data in this distribution is much more spread out. dhaussling@gmail.com