Introductory Statistics for Engineers
Introductory Statistics for Engineers STAT 224
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Mrs. Triston Collier
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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 224 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/205080/stat-224-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
Quoc Tran MSC B248D transtatwiscedu 1 Counting Technique 11 Multiplication Rule If the sets 14114114lH contain respectively nlnZnk elements there arerl1 X 712 X gtlt nk ways of choosing first an element off1 then an element ofAi and finally an element ofAk 12 Permutation The number of permutations or ordered sequences of n distinct objects taken at a time is given by n Pwnn1 r1m 13 Combination The number of combinations of n things taken r at a time is given by n nn71n7r1 n r r 14 Proposition njfvi 2 Sample vs Population 21 Sample If x1 x2 x are sampled from the population lSample mean 2Sample median examplen EX Z n l 4Sample standard deviation s 3Sample variance 32 22 Population or Random Variable 221 Discrete Random variable mass function px 1Mean ofX EX u 29g gtlt pxl 2Variance ofX VX EX L12 ZOQ Lz2 pg EX2 EX2 Generally E hX Z We 2 11709 3Standard Deviation of X 039 W Dis 2l Quoc Tran MSC B248D transtatwiscedu 2211 Example 2211 Binomial Distribution Definition Given a binomial experiment consisting of n trials the binomial random variable X of this experiment is X the number of S s among the n trials 1 N Mass function If X Bn 7rPX x bxn 7r nj x 17 7 x Mean Ll nn39 VarianceX n72391 7239 22112 Poisson distribution e712 1796 x 012 x 222 Continuous Random variabledensity function fx 1Mean ofX EX J39 xfxdx 2Variance of x VX EX M x ml f xdx Generally EhX j hxfxdx 3Standard Deviation ofX 039 W 2221 Example 2221 Exponential distribution 2e x20 fx70 otherwise Dis 22
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