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University of California - Davis

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UC-DAVISSTA 106Erin MelconSpring

STA 106 Study Guide - Spring 2019, Comprehensive Final Exam Notes - Karishma (1984 Film), Analysis Of Variance, Variance

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8 May 2019
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture 15: MAT150A_DAY15_Oct31_Lecture

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1 May 2019
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Then the following are equivalent: f is an isometry and f , f ( x ) f ( y ) = x y x , y rn. = a a = then a = b. 2 = 3 need to show f is linear. f ( x +
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 22: Conjugacy Class, American Broadcasting Company, Prime Number

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1 May 2019
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120 = (e) + (ab) + (abc) + (abcd) + (abcde) + (ab)(cd) + (abc)(de) 60 = (e) + (abc) + (abcde) + (ab)(cd) obvi wrong bc 24 does not divide 60. Each one
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 17: Platonic Solid, Cyclic Group, Axa

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1 May 2019
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 11: Coset, Normal Subgroup, Surjective Function

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1 May 2019
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Let h g be a subgroup, then h is normal a g, ah = ha. H =< (12) >= {e, (12)} eh = h (12)h = {(12), e} (13)h = {(13), (123)} (23)h = {(23), (132)} (123)
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 28: Bijection, Identity Function, Permutation Matrix

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1 May 2019
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Announcements: oh next week only, oct 1-5, mwf 4-5. Recall: elements of sn are bijective functions p = {1, , n} {1, , n, product in sn corresponds to c
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 8: Surjective Function, Group Homomorphism, Bijection

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1 May 2019
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G nite group, h g a subgroup. (lagrange) |g| Denote [g : h] called the index of h in g. To show lagrange we built an equivalence relation x y xy 1 h. W
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 14: Linear Map, Surjective Function, Unit Circle

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1 May 2019
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Enumerating the vertuces if a regular n-gon gives a homomorphism. 6 )) = (123456) hexagon on unit circle enumerated ccw starting with 1 at (1,0) 1 3 5,
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 12: Unit Circle, Dihedral Group

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1 May 2019
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Let m matn n(r) then m on i it"s columns form an orthonormal collection. {ai} form an orthonormal collection of vectors in rn today studying o2 and so2
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 4: Coset, Group Homomorphism, Permutation

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1 May 2019
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G, h nite groups gcd(|g|, |h|) = 1 ! : g h. Example (z15, +) (z4, +) order 15, 4 respectively. 115 (115) so ord (115|ord115 divisors of 15 is 1,3,5,15
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture 19: MAT150A_DAY19_Nov28_Lecture

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1 May 2019
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Example nonfaithful group action g = sn, x = r g x = (g)x (12)x = x, (123) x = x multiply by sign of the permutation. If g x = x x r, we can"t conclude
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UC-DAVISMAT 150AJosé Simental RodríguezFall

MAT 150A Lecture Notes - Lecture 10: Normal Subgroup

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1 May 2019
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G- group g1, g2 g st g1, g2 have nite order but g1g2 has in nite order. If g1g2 = g2g1 then g1g2 has nite order provided both g1, g2 have. Homework: sh
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 11: Likelihood Function, Analysis Of Variance, Complement Factor B

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1 May 2019
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If normality of errors, or equal variance by groups are violated, we can transform our data by yij. We have already seen the following transformations.
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 7: Noncentrality Parameter, F-Distribution, Type I And Type Ii Errors

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1 May 2019
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There are many ways for h0 to be false. When h0 is false, fs is know longer a known f distribution. When you calculate (estimate) power, we assume a sp
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 13: Complement Factor B, Analysis Of Variance, Interaction Model

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1 May 2019
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When a combination of factors from factor a,b have an additional e ect on y than either alone. Factor b = dosage of blood pressure med control. An inte
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 9: Type I And Type Ii Errors, John Tukey, Analysis Of Variance

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1 May 2019
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With anova, we usually want to make more than ci. 1 2, 1 3, 2 3. Typically, you decide what cis you are interested in au priori. Issue when we make k c
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 10: Analysis Of Variance, Independent And Identically Distributed Random Variables, Summary Statistics

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1 May 2019
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 6: Single-Stage-To-Orbit, F-Test, Asteroid Family

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1 May 2019
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Calculate what propotion of ssto is associated with sse, ssa. State h0 and ha h0 : i = ii = iii and ha : at least one i is di erent. Fs = 3. 592, dfnum
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 5: Single-Stage-To-Orbit, Statistical Hypothesis Testing, White Noise

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1 May 2019
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= sample error sum of squared errors x. We were deriving ssto = ssa + sse i j z x z }| { Y z2 = (x + y)2 = x2 + 2xy + y2 (yij y)2 = (yij yi. Reminder:
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 1: Dependent And Independent Variables, Analysis Of Variance, Standard Deviation

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1 May 2019
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A person, place of thing from which we measure data. Variables that have an e ect on the response variable. Let yi be drawn from a population with mean
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 3: Type I And Type Ii Errors, Standard Deviation, Analysis Of Variance

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1 May 2019
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Assumptions for (pooled) hypothesis testing for 1 2: random sample from both groups, groups independent, y1 y2 n 1 2,r 2. 2 n : 1 = 2 (population stdev
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 2: Linear Combination, Normal Distribution, Standard Deviation

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1 May 2019
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, yn be rvs denoting all possible values of a random sample of size n. Theoretical results: x yi = sample total, if y1, . Yn are independent, then: let
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UC-DAVISSTA 106Erin MelconSpring

STA 106 Lecture Notes - Lecture 4: Analysis Of Variance, Random Variable, Independent And Identically Distributed Random Variables

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1 May 2019
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Recall anova model yij = [overall mean] + [group e ect] + [individual error] Let yij = numeric, xi = categorical variable with a categories. The basic
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