Course Content

Probability Theory Mastering

## Probability Theory Mastering

1. Additional Statements From The Probability Theory

3. Estimation of Population Parameters

4. Testing of Statistical Hypotheses

# Challenge: 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:

- Use
`ddof=0`

as an argument of`np.var()`

method to calculate sample variance. - Use
`ddof=1`

as an argument of`np.var()`

method to calculate the adjusted sample variance. - Use
`.mean()`

method to estimate the expectation of sample variance.

Everything was clear?

# Challenge: 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:

- Use
`ddof=0`

as an argument of`np.var()`

method to calculate sample variance. - Use
`ddof=1`

as an argument of`np.var()`

method to calculate the adjusted sample variance. - Use
`.mean()`

method to estimate the expectation of sample variance.

Everything was clear?