2A SE

STAT206: Statistics for Software Engineering

There is this Statistics course is recommended by Soham.

Link to course notes here.

Concepts

• Error
• Mean
• Standard Deviation
• Bias
• Variance
• Monty Hall Problem
• Random Number
• Probability
  • Probability Rules → from CS50 course
  • Relative Frequency
  • Bayesian Probability
• Counting Rules (Probability)
• Independence (Statistics)
• Mutual Exclusivity
• Baseline Fallacy
• Inclusion-Exclusion Principle
• Random Variable
• Sample vs. Population
• Probability Mass Function
• Distribution
• Cumulative Distribution Function
• Bernoulli Distribution
• Binomial Distribution
• Geometric Distribution
• Memorylessness
• Indicator Variable
• Moment-Generating Function
• Skewness
• Central Limit Theorem
• Discrete Joint Distribution
• Marginal Distribution
• Multinomial Distribution
• Data Analysis and Inference
• Histogram
• Statistical Modelling
• Estimation
• Likelihood Function
• Maximum Likelihood Estimation
• Relative Likelihood Function
• Interval Estimation
• Chi-Squared Distribution
• Hypergeometric Distribution
• Student’s t-Distribution
• Confidence Interval
  • So I think the Chi-Squared Distribution and the Student’s t-Distribution really come into the picture when we start looking at getting Confidence Intervals
• Estimator
• Hypothesis Testing
  • Student’s t-Distribution
• Goodness of Fit
• Contingency Table
• Independence of Attributes
• Linear Regression
  • Gauss-Markov Theorem
  • Least Squares

This is also called a Chi-Squared test.

Motivation: Maybe there is a different proportion of left-handed and right-handed smokers. $H_0={\pi }_L={\pi }_R$ $H_1={\pi }_L\ne {\pi }_R$ Testing the proportion of L and R handed smokers, is the same as testing for the independence and attributes.

How do you calculate ei

Miscellaneous Ideas

• Data Dredging

Probability and Statistics is very powerful, but oftentimes you can be easily mistaken and misled by your intuition.

For example, if you throw two dices, you would think that the probability of getting 7 is the same as getting a 12, since everything is uniformly distributed, so thus it’s random, but no.

A big part of statistics/probability initially is to learn how to count. → OH yes, I remember this, it wasn’t from MIT6.042 but rather on Permutations and Permutations and Combinations

One super cool thing that I also learned in MIT6042.J is the Baseline Fallacy

Definitions

• Random Experiment: An experiment whose outcomes are unknown.
• Sample Space: The set of all possible outcomes in an experiment.
• Event: Any subset of a sample space.
• Probability
• Relative Frequency: $P(A)=\text{the long-term relative frequency of an event}$

Problem-Solving Insights

Splitting a problem into two parts (using an OR).

Ex: Probability that the first card is a King, and second card is Red. First part is assuming K is not red, second parenthesis is assuming K is red. $(\frac{2}{52}\cdot \frac{13}{51})+(\frac{2}{52}\cdot \frac{12}{51})$