Discrete random variables

Discrete Random Variables

• Discrete random variables
• Probability distribution tables
• Cumulative distribution function F(X)
• Expected values E(X)
• Variance, Var(X)
• Linear combinations of random variables

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

Hypothesis tests

• Test for a sample mean (still to be completed)
• Type I and II errors (still to be completed)
• t distribution
  • confidence intervals (still to be completed)
  • t-test for the mean (still to be completed)
• Chi squared test - contingency tables (still to be completed)