Introduction to Probability 1st Blitzstein Solution Manual

Product details:

• ISBN-10 ‏ : ‎ 1466575573
• ISBN-13 ‏ : ‎ 978-1466575578
• Author: Joseph K. Blitzstein

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and toolsfor understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version.

Table of contents:

Probability and Counting
Why Study Probability?
Sample Spaces and Pebble World
Naive Definition of Probability
How to Count
Story Proofs
Non-Naive Definition of Probability
Recap
R
Exercises

Conditional Probability
The Importance of Thinking Conditionally
Definition and Intuition
Bayes’ Rule and the Law of Total Probability
Conditional Probabilities Are Probabilities
Independence of Events
Coherency of Bayes’ Rule
Conditioning as a Problem-Solving Tool
Pitfalls and Paradoxes
Recap
R
Exercises

Random Variables and Their Distributions
Random Variables
Distributions and Probability Mass Functions
Bernoulli and Binomial
Hypergeometric
Discrete Uniform
Cumulative Distribution Functions
Functions of Random Variables
Independence of r.v.s
Connections Between Binomial and Hypergeometric
Recap
R
Exercises

Expectation
Definition of Expectation
Linearity of Expectation
Geometric and Negative Binomial
Indicator r.v.s and the Fundamental Bridge
Law of The Unconscious Statistician (LOTUS)
Variance
Poisson
Connections Between Poisson and Binomial
Using Probability and Expectation to Prove Existence
Recap
R
Exercises

Continuous Random Variables
Probability Density Functions
Uniform
Universality of The Uniform
Normal
Exponential
Poisson Processes
Symmetry of i.i.d. Continuous r.v.s
Recap
R
Exercises

Moments
Summaries of a Distribution
Interpreting Moments
Sample Moments
Moment Generating Functions
Generating Moments With MGFs
Sums of Independent r.v.s Via MGFs
Probability Generating Functions
Recap
R
Exercises

Joint Distributions
Joint, Marginal, and Conditional
2D LOTUS
Covariance and Correlation
Multinomial
Multivariate Normal
Recap
R
Exercises

Transformations
Change of Variables
Convolutions
Beta
Gamma
Beta-Gamma Connections
Order Statistics
Recap
R
Exercises

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