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Please enable JavaScript in your browser settings or update your browser.Challenge: Estimate Parameters of Chi-square Distribution | Estimation of Population Parameters
Advanced Probability Theory
course content

Course Content

Advanced Probability Theory

Advanced Probability Theory

1. Additional Statements From The Probability Theory
Course OverviewAbsolutely Continuous and Discrete Random VariablesCumulative Distribution Functions and Probability Density FunctionsCharacteristics of Random VariablesRandom VectorsUseful Properties of the Gaussian DistributionChallenge: Detecting Outliers Using 3-Sigma Rule
2. The Limit Theorems of Probability Theory
Law of Large NumbersLaw of Large Numbers for Bernoulli ProcessChallenge: Estimate Mean Value Using Law of Large NumbersCentral Limit TheoremChallenge: Application of the CLT to Solving Real Problem
3. Estimation of Population Parameters
General population. Samples. Population parameters.Momentum estimation. Maximum Likelihood EstimationChallenge: Estimate Parameters of Chi-square DistributionUnbiased EstimationChallenge: Checking Bias of An Estimation Using SimulationConsistent EstimationEfficient EstimationConfidence Intervals for Population ParametersChallenge: Confidence Interval for Exponential Distribution Parameter
4. Testing of Statistical Hypotheses
What is Statistic Hypothesis? Type 1 and Type 2 ErrorsWhat is P-value?Comparing Means of Two Different DatasetsChallenge: Using CLT to Compare Mean Values of Non-Gaussian DatasetsChallenge: Resampling Approach to Compare Mean Values of the DatasetsTesting the Hypothesis of Independence of Two Random Variables

bookChallenge: Estimate Parameters of Chi-square Distribution

Task

Suppose that we have samples from the Chi-square distribution. We must determine the parameter K of this distribution, which represents the number of degrees of freedom.
We know that the mathematical expectation of the Chi-square distributes value is equal to this parameter K.
Estimate this parameter using the method of moments and the maximum likelihood method. Since the number of degrees of freedom can only be discrete, round the resulting number to the nearest integer.
Your task is:

  1. Calculate the mean value over samples using .mean() method.
  2. Use .fit() method to get maximum likelihood estimation for the parameter.

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Section 3. Chapter 3
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bookChallenge: Estimate Parameters of Chi-square Distribution

Task

Suppose that we have samples from the Chi-square distribution. We must determine the parameter K of this distribution, which represents the number of degrees of freedom.
We know that the mathematical expectation of the Chi-square distributes value is equal to this parameter K.
Estimate this parameter using the method of moments and the maximum likelihood method. Since the number of degrees of freedom can only be discrete, round the resulting number to the nearest integer.
Your task is:

  1. Calculate the mean value over samples using .mean() method.
  2. Use .fit() method to get maximum likelihood estimation for the parameter.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Section 3. Chapter 3
toggle bottom row

bookChallenge: Estimate Parameters of Chi-square Distribution

Task

Suppose that we have samples from the Chi-square distribution. We must determine the parameter K of this distribution, which represents the number of degrees of freedom.
We know that the mathematical expectation of the Chi-square distributes value is equal to this parameter K.
Estimate this parameter using the method of moments and the maximum likelihood method. Since the number of degrees of freedom can only be discrete, round the resulting number to the nearest integer.
Your task is:

  1. Calculate the mean value over samples using .mean() method.
  2. Use .fit() method to get maximum likelihood estimation for the parameter.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Task

Suppose that we have samples from the Chi-square distribution. We must determine the parameter K of this distribution, which represents the number of degrees of freedom.
We know that the mathematical expectation of the Chi-square distributes value is equal to this parameter K.
Estimate this parameter using the method of moments and the maximum likelihood method. Since the number of degrees of freedom can only be discrete, round the resulting number to the nearest integer.
Your task is:

  1. Calculate the mean value over samples using .mean() method.
  2. Use .fit() method to get maximum likelihood estimation for the parameter.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 3. Chapter 3
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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