S2 Tutorials

The Poisson Distribution

Poisson Distribution

  1. Poisson distribution
  2. Changing the mean
  3. Finding an observed value x
  4. Exam Questions - Poisson distribution

Poisson Approximation to the Binomial Distribution

  1. Poisson approximation to the binomial distribution
  2. Exam Questions - Poisson approximation to the binomial distribution

Normal Approximation to the Poisson Distribution

  1. Continuity corrections
  2. The normal approximation to the Poisson distribution
  3. Exam Questions - Normal approximation to the Poisson distribution

Linear combinations of random variables

Linear combinations of random variables

  1. Linear combinations of discrete random variables
  2. E(aX + bY) = aE(X) + bE(Y)
  3. Var(aX + bY) = a2Var(X) + b2Var(Y)
  4. If X has a normal distribution then so does aX + b
  5. If X and Y have independent normal distributions then aX + bY has a normal distribution
  6. If X and Y have independent Poisson distributions then X + Y has a Poisson distribution

Continuous random variables

Probability Density Functions and Cumulative Distribution Functions

  1. What is a probability density function (p.d.f.)?
  2. Finding the constant k in a p.d.f
  3. Calculating probability from a p.d.f.
  4. The cumulative distribution function, (c.d.f)
  5. Finding the median quartiles and percentiles
  6. Finding the mode from a p.d.f.
  7. E(X) and Var(X)
  8. Exam Questions - Probability density functions and cumulative distribution functions

Estimation and Sampling

Estimation and Sampling

  1. Difference between between a sample and a population
  2. Random sampling using random number tables or calculator
  3. Simple random sampling
  4. What is a statistic?
  5. Sampling distribution of the sample mean
  6. Sampling distribution of the mode and median
  7. Exam Questions - Estimation and sampling, Median
  8. Central Limit Theorem
  9. Confidence interval for a population mean
  10. Confidence interval for a population proportion
  11. Exam Questions - Estimation and sampling, Range

Hypothesis Tests

Hypothesis Tests – Binomial Distribution

  1. Test for a binomial proportion
  2. Lower tail test
  3. Upper tail test
  4. Critical values - lower tail test
  5. Critical values - upper tail test
  6. Two tailed test
  7. Exam Questions - Hypothesis tests: binomial distribution

Hypothesis Tests – Poisson Distribution

  1. Test for a Poisson mean
  2. Lower tail test
  3. Upper tail test
  4. Two tailed test
  5. Exam Questions - Hypothesis tests: Poisson distribution
  6. Hypothesis test for the population mean
  7. Type I error and Type II errors