Stat Probability and Power

Probability and Power

The part of the statistical lesson that I went through last week that has left a profound impact on me is the Poisson Distribution of numbers and the finding out the probability based on this distribution theory and formula. The French mathematician Simeon Denis Poisson developed the Poisson Distribution in 1837 and is named after him. This distribution is used when it is safely assumed that the outcome is the number of times of an event that occurs. This form of distribution formula and theory is used to for determination of the probability of events that are rare events and it helps in giving the probability that an outcome occurs a specified number of times and when the number of trials is generally large and there is a small chance of probability of any one occurrence (Hulley, 2007).

The Poisson distribution can be used in a number of scenarios like in the planning of the number of beds that a hospital would need in the intensive care unit or the number of ambulances that would be needed on call or ascertaining the number of operators that would be required on a switchboard so that an adequate number of resources is always made available. Other rare but complex probabilities used to model the number of cells present in a given volume of any form fluid and the number of bacterial colonies that are growing in a certain amount of medium can be found out (Chan, Zee, Jayson, & Harris, 2011).

The following formula is used to represent the number of successes occurring within a given time interval or a specified or predefined region of space using the variable X is given by the following formula:

P (x; ) = (e-?) (?x) / x!

Where x = 1,2,3,

E = 2.71828 and ? = mean number of success in the given time interval or region of space (Hulley, 2007).

Another aspect of the Poisson distribution that has had an impact is the mean and variance of Poisson Distribution. In this statistical calculation, it is assumed that ? is the average number of successes occurring within a given time interval or space within the Poisson distribution which results in the mean and the variance of the Poisson distribution both being equal to ?.

Therefore what attracted me to this formula and theory is that just only one parameter -- ?, is always required to find out the probability of an event.