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Probability and statistics problem questions

Please only apply if you excel in these topics.

Topics are ;

Foundations of Probability:

•Basic Set theory; Definitions, notations, operations and Venn diagrams

• Set identities, Sample Spaces and Events

• Probability Axioms and Corollaries, Methods of Assigning Probabilities

Conditional Probability:

• Independence, Theorem of Total Probability, Bayes Rule

Sequential Experiments and Counting Principles:

•Multiplication Rule, Permutations, Combinations, Distinguishable Permutations

Discrete Random Variables and Probability Distributions:

• Probability Mass function and Cumulative Density Function; Special Discrete Random

Variables: Bernoulli, Binomial, Geometric, Poisson, Uniform Distribution

• Mathematical Expectation, Variance and Standard Deviation of Discrete Random

Variables, Properties of Expectation

Continuous Random Variables:

• PDF, CDF and properties; PDF and CDF of transformation of random variables

• Mathematical Expectation, Variance and Standard Deviation of Continuous Random

Variables; properties of expectation and variance

• Important Continuous Random Variables in Electrical Engineering: Uniform, Exponential,

Gaussian (Normal), Regular and Standard Gaussian distributions

• Q-function and Error Function; Applications and examples

Basic Reliability Calculations

• Failure distribution, Reliability function, failure rate function, mean-time-to-failure,

reliability of series and parallel systems

Bivariate random variables

• Joint PMF, PDF and CDF for Discrete and continuous random variables, Marginal

distributions: Discrete and continuous random variables

• Conditional PDF and CDF; Conditional Expectations of Discrete and continuous random

variables; Independence

• Correlation, Covariance and correlation coefficient

Sums of random variables:

• Mean and Variance of Sums of Two Random Variables

• Moment generating functions and joint PDFs of independent random variables

• The Central limit theorem

Sample statistics:

• Sample mean, variance, covariance and correlation coefficient

• Empirical Distribution, Quantile-Quantile plots and Goodness of Fit

Estimation Theory and Applications:

• Desirable properties of Estimators, The Maximum likelihood estimators

• Point and interval estimation, confidence interval

Hypotheses Testing:

• Definitions and Binary hypothesis testing

• Test concerning mean and variance; critical intervals and decision making

Introduction to Random Processes: Statistical Descriptions of Random Processes

• One random process: Mean, mean-square, variance, auto-correlation, auto-covariance

• Two random processes: cross-correlation cross-covariance

• Stationary and non-stationary random processes; Time averages and ergodicity; White

noise process

There are around 8 written problems which I need the solution to. I'll send pictures of the problem at dec 16 5:00 pm est and I need all answers by dec 16th 9:15 pm est but also answers as each question is finished.

I'll provide some reference problems and content to look at so the freelancer has idea of what kind of questions and related topics will be asked.

Færdigheder: Statistikker

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( 14 bedømmelser ) edmonton, Canada

Projekt-ID: #12521712

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