# STAT 340

## Probability and Inference 2

Statistics College of Physical and Mathematical Sciences

### Course Description

Random variables; transformations; estimation and hypothesis testing; sampling distributions; central limit theorem; law of large numbers.

### When Taught

Fall and Winter

Grade Rule 8: A, B, C, D, E, I (Standard grade rule)

3

3

3

0

### Recommended

Stat 123 and Stat 124

Transformations

### Learning Outcome

<p style="-moz-user-select: text;">Find the distribution of a transformation of random variables, including the Chi-squared and derived distributions t and F.</p>

### Title

Sampling Distributions

### Learning Outcome

<p style="-moz-user-select: text;">Explore the sampling distributions for means and totals of random samples from common distributions.</p>

Convergence

### Learning Outcome

<p style="-moz-user-select: text;">Apply convergence in probability and distribution to prove the Law of Large Numbers and participate in proving the Central Limit Theorems for means and proportions.</p>

Sufficiency

### Learning Outcome

<p style="-moz-user-select: text;">Find sufficient statistics in one-parameter problems.</p>

Point Estimation

### Learning Outcome

<p>Derive method of moments, maximum likelihood, and Bayesian estimators.</p>

### Title

Interval Estimation

### Learning Outcome

<p>Construct confidence intervals using pivots and credible intervals.</p>

Evaluation

### Learning Outcome

<p>Evaluate point estimators with respect to bias, variance, and MSE.</p>

Simulation

### Learning Outcome

<p>Examine sampling distributions and evaluate estimators using simulation.</p>

### Title

Critical Thinking

### Learning Outcome

<p>Increase analytical confidence and critical thinking skills.</p>

### Title

Hypothesis Testing

### Learning Outcome

<p>Apply the Neyman-Pearson lemma to derive the rejection region for problems involving simple hypotheses.</p>