Topic 7 – Option: Statistics and probability

Discrete Random Variables

Discrete Random Variables

  1. Expected values E(X)
  2. Variance, Var(X)
  3. Linear combinations of discrete random variables
  4. Exam Questions - Discrete random variables

Negative Binomial distribution

  1. Negative Binomial 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

Estimators

  1. Unbiased estimators and estimates
  2. Comparison of unbiased estimators based on variances

Central Limit Theorem

  1. Central Limit Theorem

Confidence intervals

  1. Confidence intervals for the mean of a normal population

Hypothesis Tests

Hypothesis Testing

  1. Null and alternative hypothesis
  2. Significance level
  3. Critical regions, critical values, p-values, one tailed and two tailed tests
  4. Type 1 and Type II errors
  5. Testing hypotheseis for the mean of a normal distribution

Correlation and Linear Regression

Correlation

  1. Correlation
  2. Product moment correlation coefficient (pmcc)
  3. Exam Questions - Correlation

Regression

  1. Regression
  2. Interpreting the regression line constants, explanatory and response variables
  3. Making predictions and reliability of predicted values
  4. Exam Questions - Regression
  5. Use of the t-statistic to test the null hypothesis that r=0