# Probability and Inference 2

Hours | 3.0 Credit, 3.0 Lecture, 0.0 Lab |

Prerequisites | STAT 240 & MATH 113 |

Recommended | Stat 123 and Stat 124. |

Taught | Fall, Winter, Spring |

Programs | Containing STAT 340 |

### 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