Probability & Statistics
At Milianns Tutors, we offer specialized tutoring services for undergraduate Probability & Statistics courses. Our goal is to help you understand and apply statistical concepts and probability theory, enhancing your analytical skills and preparing you for success in your academic and professional pursuits.
Course Overview
Descriptive Statistics
Measures of Central Tendency: Mean, median, mode, and how they summarize data sets. Measures of Dispersion: Range, variance, standard deviation, interquartile range, and their significance in understanding data spread. Data Visualization: Histograms, bar charts, box plots, scatter plots, and other graphical representations of data.
Probability Theory
Basic Concepts: Definitions of probability, sample spaces, and events. Probability Rules: Addition and multiplication rules, complementary events, and the concept of independence. Conditional Probability: Bayes' theorem, conditional probability, and their applications.
Random Variables
Discrete Random Variables: Probability mass functions (PMFs), expectation, variance, and examples like binomial and Poisson distributions. Continuous Random Variables: Probability density functions (PDFs), cumulative distribution functions (CDFs), expectation, and variance. Joint Distributions: Joint, marginal, and conditional distributions for multiple random variables.
Probability Distributions
Discrete Distributions: Binomial, Poisson, geometric, and hypergeometric distributions. Continuous Distributions: Normal, exponential, t-distribution, chi-square, and F-distributions. Properties and Applications: Understanding the properties of these distributions and their real-world applications.
Statistical Inference
Sampling Distributions: Central Limit Theorem, sampling distribution of the sample mean and proportion. Estimation: Point estimation, properties of estimators, methods of moments, and maximum likelihood estimation. Confidence Intervals: Constructing confidence intervals for population parameters and interpreting them. Hypothesis Testing: Null and alternative hypotheses, Type I and Type II errors, p-values, and power of a test.
Regression Analysis
Simple Linear Regression: Fitting a linear model, interpreting coefficients, hypothesis testing, and confidence intervals.
Multiple Regression: Extending linear regression to multiple predictors, assessing model fit, and dealing with multicollinearity.
Model Diagnostics: Residual analysis, influence measures, and model selection criteria (AIC, BIC).
Analysis of Variance (ANOVA)
One-Way ANOVA: Comparing means across multiple groups, assumptions, and interpretation.
Two-Way ANOVA: Analyzing the effect of two factors, interaction effects, and multiple comparisons.
Non-Parametric Methods
Rank-Based Tests: Wilcoxon signed-rank test, Mann-Whitney U test, Kruskal-Wallis test, and Spearman’s rank correlation.
Resampling Techniques: Bootstrapping and permutation tests for inference without relying on parametric assumptions.
Applications of Statistics
Experimental Design: Principles of designing experiments, randomization, replication, and blocking.
Quality Control: Control charts, process capability analysis, and Six Sigma.
Data Analysis in Various Fields: Applying statistical methods to problems in engineering, economics, social sciences, natural sciences, medicine, and more.