Course

MSE-213: Probability and statistics for materials science

Lectures in this course (35)

Important Distribution Functions: Bernoulli, Binomial, Uniform

Explores important distribution functions like Bernoulli, Binomial, and Uniform in probability theory.

Binomial Distribution in R

Introduces the Binomial distribution in R with examples of n coin tosses.

Normal Distribution: Basics and Applications

Covers the basics of the normal distribution and its applications in probability calculations.

Law of Large Numbers: Probability

Explores the convergence of averages of random variables and empirical frequencies in probability theory.

Central Limit Theorem

Covers the central limit theorem, showing how random processes converge to a normal distribution.

Parameter Estimation

Introduces statistical inference concepts, focusing on parameter estimation, unbiased estimators, and mean estimation using independent random variables.

Estimator of Variance

Explores variance estimation, creating personal estimators, correcting bias, and understanding Mean Square Error in statistical analysis.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

Hypothesis Testing: Statistical Disproof and Probability Calculation

Explores hypothesis testing through statistical disproof and probability calculation, emphasizing the significance level and error handling in statistical statements.

Confidence Intervals and T-Test

Explores confidence intervals, T-test, and hypothesis testing, including assumptions and critical regions.

Two-Sample T-Test

Explains the two-sample t-test for comparing means of independent samples, including hypothesis testing steps and test statistic calculation.

Chi-squared Test: Hypothesis Testing

Introduces the chi-squared test for hypothesis testing against theoretical distributions, showcasing its application with dice fairness testing.

Statistical Modeling: Fundamentals and Process Factors

Covers the fundamental concept of statistical modeling and process factors for prediction and optimization.

Introduction to ANOVA

Covers the basics of ANOVA using a case study on sleeping pill effectiveness.

Z-Test: Hypothesis Testing

Introduces hypothesis testing, focusing on the Z-test and critical regions.