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Probability and Statistics
STAT 211 (and MATH courses)
Basic probability Probability space exercise example Probability space Example: marbles from a bag Example: picking a non-blue marble Probability 1 Probability with playing cards and venn diagrams Additional rule for probabilty Compound probablity and independent events Getting at least one head Example: probability of rolling doubles Lebron asks: what are the chances of making 10 free throws in a row Lebron asks: what are the chances of three free throws versus one three pointer Frequency probability and unfair coins Example: getting two questions right on an exam Example: rolling even three times Independent probability Frequency stability Compound events Introduction to dependent probability Example: dependent probability Example: bag of unfair coins Example: is an event independent or dependent? Identifying dependent and independent events Dependent probability Multiplying dependent probabilities Monty hall problem Intersection and union of sets Relative complement or difference between sets Universal set and absolute complement Subset, strict subset, and superset Bringing the set operations together Basic set notationIntroduction to random variables CVEN 302 Probability 1 Probability with playing cards and venn diagrams Additional rule for probabilty Frequency probability and unfair coins Example: getting two questions right on an exam Independent probability Intersection and union of sets Relative complement or difference between sets Universal set and absolute complement CVEN 307 Monty hall problem Probability (part 1) CVEN 322 Probability with playing cards and venn diagrams Additional rule for probabilty Getting at least one head Introduction to dependent probability ECEN 215 Introduction to random variables STAT 211, MATH 151
Permutations Combinations Counting 2 Ways to arrange colors Example: 9 card hands Example: ways to pick officers Permutations Combinations Permuatations and combinations Example: probability through counting outcomes Example: all the ways you can flip a coin Getting exactly two heads (combinatorics) Probability and combinations (part 2) Probability using combinations Exactly three heads in five flips Example: different ways to pick officers Example: combinatorics and probability Example: lottery probability Mega millions jackpot probability Generalizing with binomial coefficients (bit advanced) Conditional probability and combinations Conditional probability warmup Birthday probability problem Probability with permutations and combinations CVEN 302 Generalizing with binomial coefficients (bit advanced) Birthday probability problem Probability with permutations and combinations STAT 211, CVEN 302, CVEN 322, ECEN 215
Correlation and causality Fitting a line to data Estimating the line of best fit exercise Estimating the line of best fit Squared error of regression line Proof (part 1) minimizing squared error to regression line Proof (part 2) minimizing squared error to regression line Proof (part 3) minimizing squared error to regression line Proof (part 4) minimizing squared error to regression line Regression line example Second regression example R-squared or coefficient of determination Calculating r-squared Covariance and the regression line |
STAT 211
Range, variance, and standard deviation as measures of dispersion Variance of a population Sample variance Review and intuition why we divide by n-1 for the unbiased sample variance Challenge: unbiased estimate of population variance Unbiased estimate of population variance Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance Simulation providing evidence that (n-1) gives us an unbiased estimate Will it converge towards -1? Variance Population standard deviation Sample standard deviation and bias Exploring standard deviation 1 module Exploring standard deviation 1 Standard deviation Statistics: alternate variance formulas Statistics: the average Statistics: variance of a population Statistics: sample variance CVEN 302, CVEN 322 Unbiased estimate of population variance Simulation providing evidence that (n-1) gives us an unbiased estimate Will it converge towards -1? CVEN 307 Range, variance, and standard deviation as measures of dispersion Variance of a population Sample variance Review and intuition why we divide by n-1 for the unbiased sample variance Challenge: unbiased estimate of population variance Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance Variance Population standard deviation Sample standard deviation and bias Exploring standard deviation 1 module Exploring standard deviation 1 Standard deviation Statistics: alternate variance formulas ALL COURSES Statistics: the average Statistics: variance of a population Statistics: sample variance STAT 211 (and MATH courses)
Random variables Discrete and continuous random variables Constructing a probability distribution for random variable Constructing probability distributions Probability density functions Expected value: e(x) Expected value Law of large numbers Term life insurance and death probability Expected value with empirical probabilities Expected value with calculated probabilities Making decisions with expected values Binomial distribution 1 Binomial distribution 2 Binomial distribution 3 Binomial distribution 4 Expected value of binomial distribution Poisson process 1 Poisson process 2 CVEN 307 Binomial distribution 1 Binomial distribution 2 Binomial distribution 3 Binomial distribution 4 CVEN 322 Term life insurance and death probability ECEN 215 Random variables STAT 211
Introduction to the normal distribution Normal distribution excel exercise Ck12.org normal distribution problems: qualitative sense of normal distributions Ck12.org normal distribution problems: empirical rule Ck12.org normal distribution problems: z-score Ck12.org exercise: standard normal distribution and the empirical rule Empirical rule Ck12.org: more empirical rule and z-score practice Z-scores 1 Z-scores 2 Z-scores 3 Central limit theorem Sampling distribution of the sample mean Sampling distribution of the sample mean 2 Standard error of the mean Sampling distribution example problem Convidence interval 1 Confidence interval example Small sample size confidence intervals Mean and variance of bernoulli distribution example Bernoulli distribution mean and variance formulas Margin of error 1 Margin of error 2 Hypothesis testing and p-values One-tailed and two-tailed tests Type 1 errors Z-statistics vs. T-statistics Small sample hypothesis test T-statistic confidence interval Large sample proportion hypothesis testing Variance of differences of random variables Difference of sample means distribution Confidence interval of difference of means Clarification of confidence interval of difference of means Hypothesis test for difference of means Comparing population proportions 1 Comparing population proportions 2 Hypothesis test comparing population prooortions Chi-square distribution introduction Pearson's chi square test (goodness of fit) Contingency table chi-square test Anova 1: calculating sst (total sum of squares) Anova 2: calulating ssw and ssb (total sum of squares within and between) Anova 3: hypothesis test with f-statistic CVEN 307 Introduction to the normal distribution Normal distribution excel exercise Ck12.org normal distribution problems: qualitative sense of normal distributions Ck12.org normal distribution problems: empirical rule Ck12.org normal distribution problems: z-score Ck12.org exercise: standard normal distribution and the empirical rule Empirical rule Ck12.org: more empirical rule and z-score practice Z-scores 1 Z-scores 2 Z-scores 3 Standard error of the mean |
Differential Equations
MATH 308
What is a Differential Equation Simple Differential Equations Seperable Differential Equations Seperable Differential Equations 2 Exact Equations Intuition 1 Exact Equations Intuition 2 Exact Equations Example 1 Exact Equations Example 2 Exact Equations Example 3 Integrating Factors 1 Integrating Factors 2 First Order Homogenous Equations First Order Homogenous Equations 2 CVEN 302, CVEN 311 Exact Equations Intuition 1 (Proofy) Exact Equations Intuition 2 (Proofy) Exact Equations Example 1 Exact Equations Example 2 Exact Equations Example 3 Integrating Factors 1 Integrating Factors 2 Homogeneous Equations Homogeneous Equations 2 CVEN 363 Seperable Differential Equations Seperable Differential Equations 2 Exact Equations Intuition 1 (Proofy) Exact Equations Intuition 2 (Proofy) Exact Equations Example 1 Exact Equations Example 2 Exact Equations Example 3 Integrating Factors 1 Integrating Factors 2 |
MATH 308
2nd Order Linear Homogeneous Differential Equations 1 2nd Order Linear Homogeneous Differential Equations 2 2nd Order Linear Homogeneous Differential Equations 3 2nd Order Linear Homogeneous Differential Equations 4 Complex Roots of the Characteristic Equations 1 Complex Roots of the Characteristic Equations 2 Complex Roots of the Characteristic Equations 3 Repeated Roots of the Characteristic Equation Repeated Roots of the Characteristic Equation Part 2 Undetermined Coefficients 1 Undetermined Coefficients 2 Undetermined Coefficients 3 Undetermined Coefficients 4 CVEN 302 2nd Order Linear Homogeneous Differential Eqn. 1 2nd Order Linear Homogeneous Differential Eqn. 2 2nd Order Linear Homogeneous Differential Eqn. 3 2nd Order Linear Homogeneous Differential Eqn. 4 CVEN 311 Undetermined Coefficients 1 Undetermined Coefficients 2 Undetermined Coefficients 3 Undetermined Coefficients 4 MATH 308
All videos CVEN 363, CVEN 445 Laplace Transform of the Unit Step Function Dirac Delta Function Laplace/Step Function Differential Equation |
Linear Algebra
PHYS 218, CVEN 221, CVEN 302, CVEN 363, CVEN 305, MATH 251, MATH 311Vector Intro for Linear Algebra
Recognizing Vector Quantities Adding Vectors Multiplying a Vector by a Scalar Vector Examples Scaling Vectors Unit Vector Notation Unit Vectors Adding and Subtracting Vectors in Rectangular Form Vector Dot Product and Vector Length Proving Vector Dot Product Properties Vector dot product and Vector Length Defining the Angle Between Vectors Cross Product Introduction Proof: Relationship between Cross Product and Sin of Angle Dot and Cross Product Comparison/Intuition CVEN 302, CVEN 322, CVEN 445 Matrix Vector Products Introduction to the Null Space of a Matrix Null Space 2: Calculating the Null Space of a Matrix Column Space of a Matrix Dimension of Null Space or Nullity Dimension of Column Space or Rank MATH 311 Parametric Representation of Vectors Linear Combinations and Span Introduction to Linear Independence More on Linear Independence Span and Linear Independence Linear Subspaces Basis of a Subspace Vector Dot Product and Vector Length Proving Vector Dot Product Properties Cross Product Introduction Dot and Cross Product Comparison Matrices: Reduced Row Echelon Form 1 Matrices: Reduced Row Echelon Form 2 Matrices: Reduced Row Echelon Form 3 Matrix Vector Products Introduction to the Null Space of a Matrix Null Space 2: Calculating the Null Space of a Matrix Null Space 3: Relation to Linear Independence Column Space of a Matrix Null Space and Column Space Basis Visualizing a Column Space as a Plane in R3 Dimension of the Null Space or Nullity Dimension of the Column Space or Rank |
CVEN 302, CVEN 445, MATH 311
Showing Relation between Basis Cols and Pivot Cols A More Formal Understanding of Functions Vector Transformations Linear Transformation Matrix Vector Products as Linear Transformations Linear Transformations as Matrix Vector Products Preimage and Kernel Example Sums and Scalar Multples of Linear Transformations More on Matrix Addition and Scalar Multiplication Linear Transformation Examples: Scaling and Reflections Linear Transformation Examples: Rotations in R2 Unit Vectors Introduction to Projections Matrix Product Examples Introduction to the Inverse of a Function Exploring the Solution Set of Ax=B Simplifying Conditions for Invertibility Deriving a Method for Determining Inverses Examples of Finding Matrix Inverse Formula for 2x2 Inverse 3x3 Determinant n x n Determinant Rule of Sarrus of Determinants Upper Triangular Determinant Determinant and Area of a Parallelogram Transpose of a Matrix Transpose of a Matrix Product Transpose of Sums and Inverse Transpose of a Vector Rowspace and Left Nullspace Visualizations of Left Nullspace and Rowspace Showing that A-Transpose x A is Invertible MATH 311
Orthogonal Complements Rowspace Solution to Ax=b Example Projections onto Subspaces Vizualizing a Projection onto a Plane A Projection onto a Subspace is a Linear Transformation Subspace Projection Matrix Example Another Example of a Projection Matrix Projection is Closest Vector in Subspace Least Squares Approximation Least Squares Examples Another Least Squares Example Introduction to Orthonormal Bases The Gram-Schmidt Process Gram-Schmidt Process Example Gram-Schmidt Process Example with 3 Basis Vectors MATH 311, CVEN 302, CVEN 445 Introduction to Eigenvalues and Eigenvectors Proof of Formula for Determining Eigenvalues Example Sovling for the Eigenvalues of a 2x2 Matrix Finding Eigenvectors and Eigenspaces Example Eigenvalues of a 3x3 Matrix Eigenvalues and Eigenspaces for a 3x3 Matrix |
For further information, please contact Dr. Kelly Brumbelow, Civil Engineering Undergraduate Student Services Office ([email protected])