Discrete random variables

Poisson Distribution

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

Normal Distribution

• The normal distribution
  • The Standard Normal Distribution Z~N(0,1) - Using tables
  • Calculating P(X<x) where x>µ
  • Calculating P(X>x) where x>µ
  • Calculating P(X>x) where x<µ
  • Calculating P(X<x) where x<µ
• Calculating the mean and standard deviation
• Exam Questions

Statistical approximations

Poisson Approximation to the Binomial Distribution

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

Normal Approximation to the Binomial Distribution

• The normal approximation to the binomial distribution

Normal Approximation to the Poisson Distribution

• The normal approximation to the Poisson distribution (still to be completed)
• Exam Questions

Estimation and sampling

• Sampling techniques (still to be completed)
• Unbiased estimates (still to be completed)
• Sampling distribution of the mean (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

• Type I and II errors (still to be completed)