Lecture 5.1

• Binomial distribution

Lecture 5.2

• Poisson distribution
• Poisson vs. Binomial
• Geometric distribution
• Negative Binomial distribution

Lecture 6.2

• Examples of density functions
• Cumulative distribution function
• Expected Value & Variance
• Conditional Probability in Continuous Case

Lecture 7.1

• Uniform Distribution: Examples
• Examples of Normal Distribution

Lecture 7.2: Standard normal distribution

• Standard normal distribution
• Finding probabilities for normal distribution

Lecture 8.1 | Part 1: Exponential distribution

• Introduction to exponential distribution
• Poisson vs exponential distribution

Mid-term Review | Part 1

• Counting principles
• Elements of probability
• Additional rule
• Multiplication rule
• Law of total probabilities
• Bayes' theorem

Mid-term Review | Part 2

• Random variables: discrete & continuous
• Mass function, frequency table
• Binomial, Negative Binomial, Poisson
• Density function, cumulative distribution
• Uniform, Normal, Exponential distributions

Lecture 9 | Limit Theorems

• Generating random values
• the Law of Large Numbers
• Central Limit Theorem

Lecture 10.1 | Joint distributions. Convariance .

• Joint distributions in discrete/continuous
• Marginal distributions
• Independent events/variables
• Covariance. Variance of sum (X+Y)

Lecture 10.2 | Distribution of sum of variables

• Convolution of distributions
• Density function of sum of two variables
• Expected values of sum of two variables

Lecture 11.1 | Introduction to Statistics

• types of Statistics: Inferential & Descriptive
• sampling methods
• levels of data measurements
• histograms

Lecture 11.2 | Types of Statistics Graphics

• Histograms, polygons, bar graph
• Dot plot, Stem plot, Scatter plot
• Pareto chart, Pie chart
• Examples of bad graphics

Lecture 11.3 | Measures of center and variance

• Measures of center: mean, median, mode
• Measures of variance: standard deviation
• Chebyshev's theorem on proportions

Lecture 12.1 | One point parameter estimation

• Inferences about population parameter
• Likelihood function, log-likelihood function
• Maximum likelihood estimates
• Likelihood functions in continuous case

Lecture 12.2: Confidence intervals for mean

• level of confidence, critical values
• error margin
• confidence intervals for mean (big-samples)

Lecture 13.1: Confidence intervals | continued

• t-distribution
• confidence intervals for mean (small-samples)
• confidence intervals for variance
• chi-squared distribution

Lecture 13.2 | Hypothesis Test. P-Values.

• null hypothesis & alternative hypothesis
• p-value: plausibility of the null hypothesis
• left-tailed, right-tailed, two-tailed
• testing hypothesis about population mean

Problem 1 | Probability & Combinatorics

Suppose that 6 cards are taken without replacement from a deck of 52 cards. What is the probability to draw 2 red cards and 4 black cards?

Problem 2 | Conditional Probability

There are three coins in a box.One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

Problem 3 | Conditional Probability

A box contains 40 batteries, 5 of which have low lifetimes, 25 of which have average lifetimes, and 10 of which have high lifetimes.Select 8 batteries randomly without replacement. What is the probability of choosing exactly 2 low, 3 average, 3 high life times batteries?