Advanced Probability Theory
Statistics and probability theory are fundamental tools in data analysis, decision-making, and scientific research. They provide a systematic and quantitative way to understand and interpret data, make predictions, and draw conclusions based on evidence. Now we will consider all additional topics necessary for Data Science and Data Analytics.Course
Gain insight into a topic and learn the fundamentalsnew
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Outcomes
Learning outcomes
Modules
Testimonials
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Codefinity advantages
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What you will learn
- Gain a comprehensive understanding of additional probability theory topics pertinent to data science and analytics.
- Develop proficiency with both absolutely continuous and discrete random variables.
- Grasp the principles of cumulative distribution functions and probability density functions.
- Explore and characterize the features of random variables and random vectors.
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There are 6 modules in this course
Statistics and probability theory are fundamental tools in data analysis, decision-making, and scientific research. They provide a systematic and quantitative way to understand and interpret data, make predictions, and draw conclusions based on evidence. Now we will consider all additional topics necessary for Data Science and Data Analytics.Now we will understand some fundamental theoretical concepts which are used in solving real live tasks: absolutely continuous and discrete random variables, probability density function, cumulative distribution function, the characteristics of a random variable, etc.
- Course OverviewPreview
- Absolutely Continuous and Discrete Random VariablesPreview
- Cumulative Distribution Functions and Probability Density FunctionsPreview
- Characteristics of Random VariablesPreview
- Random VectorsPreview
- Useful Properties of the Gaussian DistributionPreview
- Challenge: Detecting Outliers Using 3-Sigma RulePreview
The limit theorems of probability theory are fundamental laws of probability theory that are often used in practice in a wide variety of areas, such as: building confidence intervals, estimating distribution parameters, providing A/B testings, creating ensembles of ML models, etc. Now we will consider two of the most commonly used: the Law of Large Numbers and the Central Limit Theorem.
When we work with real data we usually do not know from which distribution this data was obtained. In order to determine this, we must be able to correctly estimate the parameters of this distribution and the type of distribution, which we will learn to do in this section.
- General population. Samples. Population parameters.Preview
- Momentum estimation. Maximum Likelihood EstimationPreview
- Challenge: Estimate Parameters of Chi-square DistributionPreview
- Unbiased EstimationPreview
- Challenge: Checking Bias of An Estimation Using SimulationPreview
- Consistent EstimationPreview
- Efficient EstimationPreview
- Confidence Intervals for Population ParametersPreview
- Challenge: Confidence Interval for Exponential Distribution ParameterPreview
We have already learned how to estimate the parameters of the population. But to estimate the parameter, we make an assumption about the population distribution. Can we say that our assumption is correct? How do we prove that the estimated parameters are the real parameters of the population? Can we show that two sets of samples are independent? To answer these questions, it is necessary to consider the concept of hypothesis testing.
- What is Statistic Hypothesis? Type 1 and Type 2 ErrorsPreview
- What is P-value?Preview
- Comparing Means of Two Different DatasetsPreview
- Challenge: Using CLT to Compare Mean Values of Non-Gaussian DatasetsPreview
- Challenge: Resampling Approach to Compare Mean Values of the DatasetsPreview
- Testing the Hypothesis of Independence of Two Random VariablesPreview
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