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Challenge: Checking Bias of An Estimation Using Simulation | Estimation of Population Parameters
Probability Theory Mastering
course content

Course Content

Probability Theory Mastering

Probability Theory Mastering

1. Additional Statements From The Probability Theory
2. The Limit Theorems of Probability Theory
3. Estimation of Population Parameters
4. Testing of Statistical Hypotheses

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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