# Inference

Inference
Continuous random variables (pdf, cdf, moments); sampling distributions; Central Limit Theorem; frequentist inference (estimation, intervals); Bayesian inference (estimation, intervals); simulation.
STAT
340
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites STAT 240 & MATH 113 Recommended Stat 123 and Stat 124. Taught Fall, Winter Programs Containing STAT 340
Course Outcomes

### Named Continuous Distributions

Understand assumptions and properties of named continuous univariate distributions: normal, beta, gamma, exponential

### Solve Problems

Solve problems using joint, marginal, conditional pmf and pdf

### Linear

Calculate expectation of linear combinations, covariance, correlation

### Transformations

Calculate transformations of jointly distributed random variables

### Maximum Likelihood

Solve for the maximum likelihood estimator from a SRS

### Normal Distribution

Derive properties of maximum likelihood estimators from SRS of normal distribution

### Law of Large Numbers

Apply convergence in probability and distribution to prove the Law of Large Numbers and the Central Limit Theorem

### Central Limit Theorem

Derive the 100(1-alpha)% from the pivot derived from the Central Limit Theorem

### Probabiltiy

Derive the probability of Type I and Type II Error for simple hypothesis test using test statistic derived from the Central Limit Theorem