lets say you roll 2 dice... pdf would tell you what the chance was of a getting a sum of 7 cdf would tell you what the chances of getting a sum of 7 or below
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you can find statistics on bullying on police pdf's on bullying
this pdf file has a good list. http://www.math.ups.edu/~paradise/Project%20topics.pdf
Probability density function (PDF) of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a point in the observation space. The PDF is the derivative of the probability distribution (also known as cummulative distriubution function (CDF)) which described the enitre range of values (distrubition) a continuous random variable takes in a domain. The CDF is used to determine the probability a continuous random variable occurs any (measurable) subset of that range. This is performed by integrating the PDF over some range (i.e., taking the area under of CDF curve between two values). NOTE: Over the entire domain the total area under the CDF curve is equal to 1. NOTE: A continuous random variable can take on an infinite number of values. The probability that it will equal a specific value is always zero. eg. Example of CDF of a normal distribution: If test scores are normal distributed with mean 100 and standard deviation 10. The probability a score is between 90 and 110 is: P( 90 < X < 110 ) = P( X < 110 ) - P( X < 90 ) = 0.84 - 0.16 = 0.68. ie. AProximately 68%.
Yes, in statistics, the epsilon symbol is used for maximum allowable error. http://www.liaad.up.pt/~jgama/IWKDDS/Papers/p14.pdf
The Gaussian (Normal) distribution is determined by two parameters: its mean and its variance. Each combination of these two parameters results in a different probability density function (pdf). Finding the probability based on raw scores would require values of the pdf relating to that particular combination of mean and variance. The pdf for the Gaussian distribution is not simple to calculate and it would be impossible to tabulate infinitely many of them. Instead, only the pdf for the Z-scores - the Standard Normal pdf - is tabulated. Any raw score is converted to a Z-score and the probability evaluated from the tables.