Statistical Programming Notes - Class 1

Basics

• Probability - Study of randomness and uncertainty
• Random Experiment - Process whose outcome we cannot say predictably
• Sample Space - All possible outcomes
• Event - Subset of Sample Space
• Probability Value - Expected occurence of outcome

Concept #1
Frequentist View 

P(Event) = Number of Times Expected Event Occured / Total Number of Events
P(A) = N(A) / N

Probability P of an uncertain event A, written P(A), is defined by the frequency of that event based on previous observations

More Reads on this topic
Frequentism and Bayesianism: A Practical Introduction

Concept #1.1
Bayesian - Assign based on Intuition

Concept #2 - Conditional Probability
P(E) occurring given that another dependant event has already occurred

P(A/B) = P(A Intersection B) / P(B)

More Read - Link

Bayes Theorem
Three production lines
48% Red - 6% Production Line Defective
31% Blue - 11% Production Line Defective
21% White - 8% Production Line Defective

P(R/D) = P(R Intersection D) / P(D)

P(R) = .48
P(D/R) = 0.06
P(D) = P(D/R)P(R) + P(D/W)P(W) + P(D/B)P(B)

P(R/D) = P(R Intersection D) / P(D)

P(R/D) = P(R Intersection D) / (P(D/R)P(R) + P(D/W)P(W) + P(D/B)P(B))

Concept #5
Independent Events - Independent Events are not affected by previous events

Dependent Events - Taking coloured marbles from a bag: as you take each marble there are less marbles left in the bag, so the probabilities change.

Independent Events - Taking and replacing coloured marbles from a bag: as you take each marble there are same marbles left in the bag, so the probabilities won't change.

R Programming Concepts

• R - Interpreted language
• Assignment operator =, <-
• Vector - Same as Arrays in other languages
• B <- matric(c(2,4,3,1,5,7) nrow = 3, ncol = 2). matrix(rows, columns)
• In Matrix - Data Filled in columnar manner
• matrix columnar, rowwise operations possible using apply command apply(b,2,mean) - Columnar mean, apply(b,1,mean) - rowwise mean
• Data Frame - Way to store different types of columns, Values in one particular column need to be of same data type

Happy Learning!!!