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Please enable JavaScript in your browser settings or update your browser.Challenge: Checking Bias of An Estimation Using Simulation | 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: Checking Bias of An Estimation Using Simulation

In the last chapter, we covered the concepts of sample variance and adjusted sample variance. Now let's see how with the help of simulation, we can determine that the first estimation is biased and the second is unbiased.

We will use the Gaussian population: we will build an estimate of the sample variance and the adjusted sample variance on different subsets of the population. Next, using the law of large numbers, we will estimate the mean of the sample variance and the adjusted sample variance and compare it with the real variance of the population.

Task

Your task is to perform simulations to obtain the value of the sample variance, and the adjusted sample variance for 2000 different subsets of the population and compare the mean of the sample variance and the adjusted sample variance with the real value of the population mean:

  1. Use ddof=0 as an argument of np.var() method to calculate sample variance.
  2. Use ddof=1 as an argument of np.var() method to calculate the adjusted sample variance.
  3. Use .mean() method to estimate the expectation of sample variance.

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Section 3. Chapter 5
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bookChallenge: Checking Bias of An Estimation Using Simulation

In the last chapter, we covered the concepts of sample variance and adjusted sample variance. Now let's see how with the help of simulation, we can determine that the first estimation is biased and the second is unbiased.

We will use the Gaussian population: we will build an estimate of the sample variance and the adjusted sample variance on different subsets of the population. Next, using the law of large numbers, we will estimate the mean of the sample variance and the adjusted sample variance and compare it with the real variance of the population.

Task

Your task is to perform simulations to obtain the value of the sample variance, and the adjusted sample variance for 2000 different subsets of the population and compare the mean of the sample variance and the adjusted sample variance with the real value of the population mean:

  1. Use ddof=0 as an argument of np.var() method to calculate sample variance.
  2. Use ddof=1 as an argument of np.var() method to calculate the adjusted sample variance.
  3. Use .mean() method to estimate the expectation of sample variance.

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 5
toggle bottom row

bookChallenge: Checking Bias of An Estimation Using Simulation

In the last chapter, we covered the concepts of sample variance and adjusted sample variance. Now let's see how with the help of simulation, we can determine that the first estimation is biased and the second is unbiased.

We will use the Gaussian population: we will build an estimate of the sample variance and the adjusted sample variance on different subsets of the population. Next, using the law of large numbers, we will estimate the mean of the sample variance and the adjusted sample variance and compare it with the real variance of the population.

Task

Your task is to perform simulations to obtain the value of the sample variance, and the adjusted sample variance for 2000 different subsets of the population and compare the mean of the sample variance and the adjusted sample variance with the real value of the population mean:

  1. Use ddof=0 as an argument of np.var() method to calculate sample variance.
  2. Use ddof=1 as an argument of np.var() method to calculate the adjusted sample variance.
  3. Use .mean() method to estimate the expectation of sample variance.

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!

In the last chapter, we covered the concepts of sample variance and adjusted sample variance. Now let's see how with the help of simulation, we can determine that the first estimation is biased and the second is unbiased.

We will use the Gaussian population: we will build an estimate of the sample variance and the adjusted sample variance on different subsets of the population. Next, using the law of large numbers, we will estimate the mean of the sample variance and the adjusted sample variance and compare it with the real variance of the population.

Task

Your task is to perform simulations to obtain the value of the sample variance, and the adjusted sample variance for 2000 different subsets of the population and compare the mean of the sample variance and the adjusted sample variance with the real value of the population mean:

  1. Use ddof=0 as an argument of np.var() method to calculate sample variance.
  2. Use ddof=1 as an argument of np.var() method to calculate the adjusted sample variance.
  3. Use .mean() method to estimate the expectation of sample variance.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 3. Chapter 5
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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