# STAT 240

## Probability and Inference 1

Statistics College of Physical and Mathematical Sciences

### Course Description

Set theory; probability; principles of counting; random variables; mathematical expectation; sampling distributions; point estimation.

Fall and Winter

3

3

3

0

### Recommended

It is strongly suggested that STAT 130 and MATH 113 be taken concurrently with or before STAT 240.

Sample Spaces

### Learning Outcome

<p>Apply fundamentals of set theory, set operations, and counting to specify/enumerate events in a discrete sample space.</p>

Probability

### Learning Outcome

<p>Use the axioms of probability, conditional probability, independence, and Bayes' theorem in probabilistic calculations.</p>

### Title

Discrete Random Variables

### Learning Outcome

<p>Use probability mass functions for discrete random variables and transformations of discrete random variables.</p>

### Title

Continuous Random Variables

### Learning Outcome

<p>Use probability density and cumulative distribution functions to compute probabilities for continuous random variables.</p>

### Title

Expectation and Moments

### Learning Outcome

<p>Find and interpret expectations of random variables and functions of random variables; use moment generating functions.</p>

### Title

Named Distributions

### Learning Outcome

<p>Understand the assumptions and properties of named distributions: binomial, Poisson, uniform, exponential, normal, and gamma.</p>

### Title

Joint Distributions

### Learning Outcome

<p>Find probabilities and expectations for joint, marginal, and conditional distributions.</p>

Correlation

### Learning Outcome

<p>Calculate expectation of linear combinations, covariance, and correlation.</p>

### Title

Probabilistic Thinking

### Learning Outcome

<p>Apply tools of probability to quantitatively frame and solve problems involving uncertain outcomes.</p>

Simulation

### Learning Outcome

<p>Verify probabilistic calculations via simulation.</p>