Distribution Types and Their Validity
Distribution Types and Their Validity ENGR 0020: Probability and statistics for Engineers I
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This 3 page Class Notes was uploaded by Emily Binakonsky on Friday March 6, 2015. The Class Notes belongs to ENGR 0020: Probability and statistics for Engineers I at University of Pittsburgh taught by Maryam Mofrad in Spring2015. Since its upload, it has received 127 views. For similar materials see Probability and Statistics for Engineers 1 in Engineering and Tech at University of Pittsburgh.
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Date Created: 03/06/15
Distribution Types Emily Binakonsky I Distribution Types A ChiSquared distribution Is when the variable 52 is the variance of a random sample of size n having a normal distribution with variance 02 and degrees of freedom 12 n 1 The statistic is given by the formula II X2 n 1st x gt02 02 1 02 1 B T Distribution Use this type when given a Distribution of the Sample Mean with an Unknown 02 Letting X1X2 ane independent random variable that are all normally distributed with a mean of u and a standard deviation of a 1 n 1 n X Xi andS2 2Xi X2 n n 1 l1 l1 X M Let random variable T T With a degree of freedom 12 n 1 TE C F Distribution If 512 and 522 are the variance of two independent random samples of sample sizes n1 and n2 taken from normally distributed populations with variance of and 022 then the statistic is 2 S1 2 2 2 F 51 0251 T 2 T0252 2 1 2 2 52 With degrees of freedom v1 2 n1 1 and v2 2 n2 1 D Normal QuantileQuantile plot A plot of the ordered observations yi against the corresponding normal distribution s quantile Classic Estimation Methods take a sample find the sample mean and sample variance a Notation 1 9 denotes interest parameter Distribution Types Emily Binakonsky 2 denotes the statistic 3 g denote the statistical value b Unbiased Estimators A statistic G os am unbiased estimator of 9 if 19 E 9 for all values of 9 The difference of E9 is called the bias of G c Interval Estimation An interval estimate ofthe population parameter 9 is given by the formula 92lt9lt 5 Different pulled samples from the same population will give different values of the estimator O we can calculate a probability that a we will pick a sample that produces an interval containing the true population parameter 9 L Uis is called the 1001 00 Confidence Interval The confidence coefficient degree of confidence is 1 a The endpoints 92 and 917 are the confidence limits Distribution Types Emily Binakonsky d Mean Estimation determining the confidence interval Step 1 Setup the probability statement to represent 1 a on values X u Step 2 Z 2 gt Rearrange for a iq Case 1 Use the Normal Distribution Case 2 Use the TDistribution Case 3 Use the ChiSquared Distribution Make sure to mention the Central Limit Theorem
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