1. Descriptive Statistics: Samples and population, Percentiles and Quartiles, Measures of central tendency and variability, Grouped data and frequency distributions, Histogram and the polygon line, Skewness and kurtosis, Chebyshev’s theorem, Methods of displaying the data, Pie and bar charts, Box plots etc.
2. Probability: Random experiment, Elementary outcome, Sample space and events, Classical definition of probability, Probability as the limit of relative frequency, Subjective probability, Axioms and rules for probability, Conditional probability, Joint and marginal probabilities, Independent events, The law of total probability and Bayes’ theorem
3. Random variables: Discrete random variables, Probability distribution and cumulative distribution function, Expected value and standard deviation of a random variable, Bernoulli and Binomial random variables, The Poisson distribution, The negative Binomial Distribution, The Geometric and Hypergeometric distribution, Continuous random variables, Probability density function, The Uniform and Exponential distributions
4. The Normal distribution: Properties of the Normal distribution, The Standard Normal distribution, Finding probabilities of the Standard Normal distribution, Transforming a Normal random variable to the Standard Normal, The inverse transformation, Normal approximation of Binomial and Poisson distributions
5. Sampling distributions: Sample statistics as estimators of population parameters, Sampling distribution of the sample mean, Central Limit Theorem, Student-t distribution, Sampling distribution of the variance, Chi-squared and F distributions
6. Confidence intervals: Confidence intervals for the population mean when the population variance is known and when the population variance is unknown, Confidence intervals for the population proportion, Confidence intervals for the population variance
7. Hypothesis testing: The Null and Alternative hypotheses, Significance level, Type I and II errors, P ower of the test, Hypothesis testing for the population mean, the population variance and the population proportion