STAT Final Study Guide
STAT Final Study Guide STAT 1053
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This 4 page Study Guide was uploaded by Morgan Routman on Sunday May 3, 2015. The Study Guide belongs to STAT 1053 at George Washington University taught by Professor Balaji in Winter2015. Since its upload, it has received 147 views. For similar materials see Intro to Statistics for Social Sciences in Statistics at George Washington University.
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Date Created: 05/03/15
STATS 1053 Final Study Guide 5315 1144 AM o A random variable is continuous if it can assume any value over an interval 0 Distribution 0 How do we describe it 0 Cannot describe the probability for each possible value because they are infinite n Shows how the probability is distributed over a range of random variables a Total area under the curve total probability 1 Represents area at the height of the curve Fx 2 0 ffXCX 1 9 area under curve 1 Pxa 0 Pxgta PxZa Pxlta PxSa Paltxltb area under fx between a and b Fx 1dc for ch3d 000000 0 All standard normal random variables are connected to Z via the following equation PZa 0 PZlta PZSa PZgt0 05 PZlt0 P1ltZlt1 68 P2ltZlt2 95 P3ltZlt3 997 PZgta PZlta PaltZlt0 POltZlta PaltZlta 2P0ltZlta PZgta 1Pzlta 5 POltZlta Normal Distribution Continued 0 Almost all of Z lies between 3 and 3 0 Example compute the following using zscore sheet a PZlt226 b P1ltZlt1 c PZgt12 a 04881 b 06826 c 05038901151 0 Remark 0 Note that PZgt31 0 0 Remark 0 Note that if X is normal with mean u and standard deviation 0 then PaltXltb Pauo ltZlt buo Normal Approximation to Binomial 0 Suppose X is a Binomial Random Variable with a large n 0 Steps to compute probabilities Find uno and onpq nnumber pprobabiity q1 probability Check npgt5 and nqlt5 Express probability if form PXSa or PXSbPXSa D PXSa PZSaM0 n X binomial np n n gt30 n np gt5 n nq gt5 Therefore x is approximately normal with unp and onpq for any positive integer aSn 39 XSa PZSaM0 Assessing Normality 0 Construct a histogram or a stem and leaf plot for the data 0 If normal then it ll look similar to a bell curve 0 Therefore the percent of measurements that fall within 1 2 3 Standard Deviations is 68 95 and 100 respectively 0 Should have an IQR of approximately 13 Sampling Distributions Parameter 0 Numerical descriptive measure of the population 0 Sample Statistic 0 Numerical descriptive measure of the sample 0 Theorem 1 0 Mean of the sampling distribution STAT 1053 Week 8 Continued 5315 1144 AM Example compute the following using zscore sheet a PZlt226 b P1ltZlt1 c PZgt12 a 04881 b 06826 c 05038901151 0 Remark 0 0 Remark
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