Probability Theory: Axioms of Probability:Explain the three axioms of probability and provide examples to demonstrate each. Bayes' Theorem:State Bayes' Theorem. How does it help in revising probabilities in light of new information? Provide a real-life scenario to illustrate its application. Law of Total Probability:Define the Law of Total Probability. How is it useful in solving complex probability problems? Random Variables:Differentiate between discrete and continuous random variables. Provide examples of each from real-life scenarios. Expected Value and Variance:Derive the formula for the expected value and variance of a discrete random variable. How are they interpreted in practical problems? Probability Distributions:Define the following probability distributions and give an example of where each might be applicable: Binomial Distribution Poisson Distribution Normal Distribution Exponential Distribution Central Limit Theorem (CLT):State and explain the Central Limit Theorem. Why is it fundamental to inferential statistics? Joint and Marginal Probability:Define joint probability and marginal probability. How are they related? Explain with a two-variable example. Markov Chains:What is a Markov chain? Describe its key properties and give an example where it can be applied. Conditional Probability vs. Independent Events:How do you distinguish between conditional probability and independent events? Provide an example of each. No AI use, handwritten is good if u can. Also give visuulaization for all using graphs

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 15E: Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one...

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Probability Theory:

Axioms of Probability:
Explain the three axioms of probability and provide examples to demonstrate each.
Bayes' Theorem:
State Bayes' Theorem. How does it help in revising probabilities in light of new information? Provide a real-life scenario to illustrate its application.
Law of Total Probability:
Define the Law of Total Probability. How is it useful in solving complex probability problems?
Random Variables:
Differentiate between discrete and continuous random variables. Provide examples of each from real-life scenarios.
Expected Value and Variance:
Derive the formula for the expected value and variance of a discrete random variable. How are they interpreted in practical problems?
Probability Distributions:
Define the following probability distributions and give an example of where each might be applicable:
- Binomial Distribution
- Poisson Distribution
- Normal Distribution
- Exponential Distribution
Central Limit Theorem (CLT):
State and explain the Central Limit Theorem. Why is it fundamental to inferential statistics?
Joint and Marginal Probability:
Define joint probability and marginal probability. How are they related? Explain with a two-variable example.
Markov Chains:
What is a Markov chain? Describe its key properties and give an example where it can be applied.
Conditional Probability vs. Independent Events:
How do you distinguish between conditional probability and independent events? Provide an example of each.

No AI use, handwritten is good if u can. Also give visuulaization for all using graphs

Statistics that allow for inferences or estimates about the population. Inferential statistics enable analysts come to conclusions about the population based on sample data. Inferential statistics cover the basics of inferential statistics, all kinds of hypotheses tests and their confidence intervals, design of experiments, and statistical power and errors. It also includes point estimation techniques, limit theorems, sampling distributions, approximations, and bounds. Correlation, regression, and association are also covered under inferential statistics to infer relationships between variables.

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