PRIN OF STATISTICS I
PRIN OF STATISTICS I STAT 211
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This 5 page Class Notes was uploaded by Celestino Bergnaum on Wednesday October 21, 2015. The Class Notes belongs to STAT 211 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/225762/stat-211-texas-a-m-university in Statistics at Texas A&M University.
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Date Created: 10/21/15
Crib Sheet for Exam 1 Statistics 211 1 Chapter 1 Descriptive Statistics Sample Average Population Average 7 n N 1 11 WEi1Ii To caluclate the plth percentile up 1 Let Ia refer to our data set in ascending order 2 Let ip min100 3 Find the rst index i such that i gt 23917 4 The p7th percentile is then xz1xz 7 1M 72 1f 2 1 2p 1039 otherW1se A awvAWLgt Chebychev7s Rule The proportion of observations that are Within k standard deviations pk of the mean is at least 1 Pk 1 i E 2 Chapter 2 Probability Multiplication rule Permutation Combination n1Xn2Xn2Xle Pkn For any two events A and B PA U B PA PB 7 PA O B The conditional probability of A given that B occurred PB gt 0 PAlB Two events A and B are independent if P A13 PM If A and B are independent then PA O B PAPB If A7 B7 C7 D7 are mutually independent then PA O B O C O PAPBPCPD H 3 Chapter 3 Discrete PDF s Ele M 21101 X65 EhXl was Z hX 101 X65 EaX b aEX 12 VX a2 7 102 EXESltI W2 39PW ElXZl Ele2 VaX b a2VX a202 31 Binomial Distribution For X N binomialnp n xed number of trials p probability of succes S I number of successes S PXz ltZgtp17pnix 1071727Hi7n M Ele 71 Vle EM 7 02 711017 p 3 2 Multinomial Distribution For X N multinomialnp1i i i 71m n Number of trials 7 Number of possible outcomes pi POutcome i on any particular trial 11 Number of trials resulting in outcome it 7 11 052 m 117127 i i 7 107 zllzgl i i i zrlpl p2 H pT zi0l2iu zlzguizrr 33 Hypergeometric Distribution For X N hypergemetric n M N n sample size M number of S in the population N population size I number of S in the sample M NiM POM 15184 Wherez max0n7NM S I S minnMl EX M nMnp Where p N Vle a2 N gtnlt17gt 71371100 10 34 Binomial Approximation to the Hypergeometric If we sample With replacement of if n is small relative to N and M we can approximate the Hypergeometric distribution by using the binomial distribution With p z X N hypergemetricn M N A X N binomialn p 35 Hypergeometric Distribution for k Cells N items are partitioned into k cells A1 A2 l l Ak with al a2 l l ak elements respectively Then the probability distribution ofthe random variables X1 X2 l l Xk representing the number of elements selected from A1 A2 l Arc in a random sample of size n is 1 2 kl PX1 zlX2 12MXk zk n Where For the case k 2 5 success F failure M number of S in A1 N 7 M number of F in A2 sample size population size 2333 36 Negative Binomial Probability Distribution For X N negative binomial7quot7 p number of S 7 p probability of S I the number of failures preceding the T7th success 7 l PXzltIT1 gtprlipx 1071727l T 7 7 7 T0717 1 3le 7 M 7 T011 VX a2 717217 If 7 l we have a Geometn39c distributionl PXzplipx 1071727l 37 Poisson Distribution For X N poissonA A the rate per unit time or rate per unit area I the number of successes occurring during a given time interval or in a speci ed region 7A x PXze VA x012m Agt0 L Ele M VX 02 38 Poisson Approximation to the Binomial Distribution Let X be a binomial random variable With probability distribution X N binomialn7 10 When n A 00 and p A 0 and A np remains xed at A gt 07 then X N binomialnp A X N poissonA np As a rule of thumb7 this approximation can be safely applied if nZlOO p301 np 20 4 Chapter 4 Continuous PDF s PaS X S b bfzdz Fltzgt PltX z E fydy Pa X s b Fan 7 F00 F X f I For 0 S p S l the 100p7th percentile of a continuous distribution you must solve p Fz for z where z is the 100p7th percentile Ewan hltzgt fltzgtdz Ele M flierKIWI EltX e m a2 mm 7 u fltzgtdz Remember EX 7 m2 EX2 7 EX2 a2 41 The Uniform Distribution The family of uniform distributions has the following PDF 1 fzAB 53 ASE SB otherwise 411 The Exponential Distribution The family of exponential distributions has the following PDF Ae z 2 0 gt 0 I M 7 0 otherwise
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