Math 201 notes week 3 Probability and normal distribution
Math 201 notes week 3 Probability and normal distribution STAT-201
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Popular in Statistics
This 2 page Class Notes was uploaded by Jessica Namesnik on Saturday September 17, 2016. The Class Notes belongs to STAT-201 at Colorado State University taught by Kirk Ketelsen in Fall 2016. Since its upload, it has received 4 views. For similar materials see General Statistics in Statistics at Colorado State University.
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Date Created: 09/17/16
9/13/16 Statistics 201: Probability and normal distribution Random event something that may or may not occur, and that we can assign a probability to. Examples: a coin might fall on heads tomorrow might snow the broncos might win the super bowl Gryffindor might win the house cup Random variable “x” , i.e. the roll of a die Complement is the nonoccurrence or opposite of an event. Examples: coin might fall on tails tomorrow might not snow broncos could lose the superbowl Gryffindor might lose the house cup Probability – quantifying the likelihood of a random event occurring, usually percentages(i.e. 50%), formally proportions (i.e.0.5). Must be between 0 (impossible) and 1 (certain) ( both are rare) Relative frequency how often an event occurs as a proportion of how often it could potentially occur states that probability of an outcome is the proportion of times the outcome would occur over the long run ( if we were to keep repeating a random process indefinitely). Doesn’t need to have a sample size or a denominator Probability notation p(x) is probability that event x occurs. 1p(x) is the probability event x doesn’t occur ( the complement) Standardization finding distance from mean in terms of standard deviations (given a common unit) Zscore value that has been standardized in this manner. shows if data point lies above or below the mean. (+) zscore= above () zscore= below Magnitude shows how far the data point is from the mean in terms of standard deviations. We say that they are unitless, but they are expressed in terms of distance from the mean. Z=(xxx)/s is the value to be standardized. xx is the population mean. S is the sample standard deviation. xx and s are sample statistics, denoted w/English letters 9/15/16 Chebyshev’s rule at least (1(1/k ) x 100% of values in a standard distribution bust lie w/in k of standard deviations of the mean. Applies to any distribution. Bell curve/Gaussian distribution most common, any variable that follows a normal distribution is said to be normally distributed. Empirical rule what % of values of a normal distribution of variables fall within 1,2,3 standard deviations of the mean. Basically the same as Chebyshev’s rule, but only applies to normal distributions.
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