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Math 201 notes week 3 Probability and normal distribution

by: Jessica Namesnik

Math 201 notes week 3 Probability and normal distribution STAT-201

Marketplace > Colorado State University > Statistics > STAT-201 > Math 201 notes week 3 Probability and normal distribution
Jessica Namesnik

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About this Document

These notes cover the lecture from 9/13-15/16
General Statistics
Kirk Ketelsen
Class Notes
Statistics, Probability
25 ?




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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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