Course Content

Probability Theory Mastering

## Probability Theory Mastering

# Challenge: Estimate Mean Value Using Law of Large Numbers

Task

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 provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.

Task

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 provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.

Everything was clear?

# Challenge: Estimate Mean Value Using Law of Large Numbers

Task

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 provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.

Task

**independent and identically distributed**, but we do not know the characteristics.

**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

cannot provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.

Everything was clear?

# Challenge: Estimate Mean Value Using Law of Large Numbers

Task

**independent and identically distributed**, but we do not know the characteristics.

**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

cannot provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.

Task

**independent and identically distributed**, but we do not know the characteristics.

**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

cannot provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.

Everything was clear?

Task

**independent and identically distributed**, but we do not know the characteristics.

**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

cannot provethat 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.

Your task is to:

- Plot histogram using
`.hist()`

method of`matplotlib.pyplot`

module. - Calculate the mean over a given subsample in
`mean_value`

function using`.mean()`

method. - Pass
`exp_samples`

as an argument of a function to calculate mean values over all subsamples. - Print the estimated mean value of all samples as the last value of
`y`

array.