Discrete random variables

Binomial Distribution

• Introduction
• Formula
  • An example for you to try
• Cumulative Probability Tables
  • For p less than or equal to 0.5
  • For p greater than 0.5
• Mean and variance

Exam Questions

Poisson Distribution

• Introduction
• Changing the mean
• Finding an observed value x

Exam Questions

Continuous random variables

Probability Density Functions and Cumulative Distribution Functions

• What is a Probability Density Function (p.d.f,)?
  • Finding the constant k in a p.d.f
  • Calculating probability from a p.d.f.
  • The cumulative distribution function, (c.d.f)
    • Harder example on the c.d.f. function
  • Finding the median from a p.d.f.
    • An example for you to try
  • Finding the mode from a p.d.f.
  • E(X) and Var(X)
    • An example for you to try
• Exam Questions

Continuous Uniform / Rectangular Distribution

• The uniform distribution - introduction
• Example on defining the pdf, calculating probabilities and quartiles
• Expected mean E(X), the variance Var(X), cumulative distribution function F(X)
• Proof of E(X)
• Proof of Var(X)
• Exam Questions

Statistical approximations

Poisson Approximation to the Binomial Distribution

• Poisson approximation to the Binomial distribution
  • An example for you to try
• Exam Questions

Continuity Corrections

• Continuity Corrections

Normal Approximation to the Binomial Distribution

• The normal approximation to the binomial distribution (old video)
• The normal approximation to the binomial distribution (updated video)
• Exam Questions

Normal Approximation to the Poisson Distribution

• The normal approximation to the Poisson distribution
• Exam Questions

Estimation and sampling

• Sampling techniques (still to be completed)
• Unbiased estimates (still to be completed)

Hypothesis tests

Binomial Distribution

• Introduction
  • Lower tail test
  • Upper tail test
  • Critical values - lower tail test
  • Critical values - upper tail test
  • Two tailed test
• Exam Questions

Poisson Distribution

• Test for a Poisson mean
  • Lower tail test
  • Upper tail test
  • Two tailed test
• Exam Questions