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## Notes from Monday's lecture

by: Emily Binakonsky

107

0

2

# Notes from Monday's lecture ENGR 0020: Probability and statistics for Engineers I

Emily Binakonsky
Pitt
Probability and Statistics for Engineers 1

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Definitions, formulas and notes on Chi-squared distributions, T-distributions and F-distributions.
COURSE
Probability and Statistics for Engineers 1
PROF.
TYPE
Class Notes
PAGES
2
WORDS
KARMA
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## Popular in Engineering and Tech

This 2 page Class Notes was uploaded by Emily Binakonsky on Friday February 27, 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 107 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: 02/27/15
Fundamental Sampling Distributions Emily Binakonsky and Data Descriptions 1 Sampling Statistics Distribution a Sampling Distribution of the difference between two means if independent samples of size n1 and n2 are drawn at random from two populations discrete or continuous with means 11 and a2 and variances and 012 and 022 respectively then the sampling distribution of the differences of means X1 X2 is approximately normally distributed with a Mean mil 2 1 2 0f 2 022 And variance of X 1 2 n1 712 X 1 2 1 2 is approx astandard normal variable 2 2 2 n n Thus Z ChiSquared Distribution If S 2 is the variance of a random sample of size n taken from a normal population having the variance 02 then the statistic has a chisquared distribution with v n 1 degrees of freedom with the statistic as n 152 quot 02 2 i1 2 Xi 252 X 02 TDistribution Let X1X2 Xn be the independent random variables that are all normal with mean u and standard deviation 6 Let 1 n 2 1 n 2 X i1Xi 5 Ezi1XiX Then the random variable T X has a tdistribution with TH 17 n 1 desgrees of freedom Let tv denote the density function curve for v degrees of freedom 0 Each tv curve is centered at 0 and bellshaped 0 Each tv curve is spread out more than the standard normal curve VlT orv gt 2 here Tt v2f W 17 0 As z increases the tv curve Spread decreases 0 As 12 gt 00 the 15 sequence approaches the standard normal curve Fundamental Sampling Distributions Emily Binakonsky and Data Descriptions d FDistribution The F statistic is defined to be the ratio of two independent chisquared random variables each divided by its degrees of freedom 3 Where U and V are independent random variables having F chisquared distributions v1 and vzdegrees of freedom How to write a foo v1 v2 for foo with 121 and 122 degrees of freedom 1 072771 if Si and 8 are the variances of independent random samples 13 05071 772 of size n1 and n2 taken from normal populations with variances 0 and 0 respectively then 2 2 F 0 0251 2 withv1n1 1cmdv2n2 1 2 2 2 0152

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