Challenge: Estimate Mean Value Using Law of Large Numbers | The Limit Theorems of Probability Theory
Probability Theory Mastering

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

Challenge: Estimate Mean Value Using Law of Large Numbers

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.

Everything was clear?

Section 2. Chapter 3

Challenge: Estimate Mean Value Using Law of Large Numbers

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.

Everything was clear?

Section 2. Chapter 3

Challenge: Estimate Mean Value Using Law of Large Numbers

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.

Everything was clear?

Assume that we have some data samples: we know these samples are independent and identically distributed, but we do not know the characteristics.

Your task is to use the law of large numbers to estimate the expected value of these samples.
We will also try to check the assumption that our data has exponential distribution: we will build a histogram based on our data and compare it with the real PDF of the exponential distribution.

Note

Visualization cannot prove that the data is distributed in a certain way. For this, it is necessary to use statistical tests, which will be considered in the last section of this course; however, with the help of visualization, we can at least roughly determine which class of distributions our data belongs to.

1. Plot histogram using `.hist()` method of `matplotlib.pyplot` module.
2. Calculate the mean over a given subsample in `mean_value` function using `.mean()` method.
3. Pass `exp_samples` as an argument of a function to calculate mean values over all subsamples.
4. Print the estimated mean value of all samples as the last value of `y` array.