# Tutor Service: Probability

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## Probability

• Estimating probabilities using simulation
• Mutually exclusive events and unions of events
• Conditional probability
• Independent versus dependent events and the multiplication rule

## Sampling distributions

• The normal distribution, revisited
• The central limit theorem
• Biased and unbiased point estimates
• Sampling distributions for sample proportions
• Sampling distributions for differences in sample proportions
• Sampling distributions for sample means
• Sampling distributions for differences in sample means

## Random variables and probability distributions

• Introduction to random variables and probability distributions
• Mean and standard deviation of random variables
• Transforming random variables
• Combining random variables
• Introduction to the binomial distribution
• Parameters for a binomial distribution
• The geometric distribution

## Inference for quantitative data: Means

• Constructing a confidence interval for a population mean
• Setting up a test for a population mean
• Carrying out a test for a population mean
• Confidence intervals for the difference of two means
• Testing for the difference of two population means

## Inference for categorical data: Proportions

• Introduction to confidence intervals
• Confidence intervals for proportions
• The idea of significance tests
• Setting up a test for a population proportion
• Carrying out a test for a population proportion
• Concluding a test for a population proportion
• Potential errors when performing tests
• Confidence intervals for the difference of two proportions
• Testing for the difference of two population proportions