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Please enable JavaScript in your browser settings or update your browser.Challenge: Application of the CLT to Solving Real Problem | The Limit Theorems of Probability Theory
Advanced Probability Theory
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Contenido del Curso

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: Application of the CLT to Solving Real Problem

Let's imagine that we need to solve the following problem:

  1. Suppose that we come to the shooting range and start shooting, the probability of hitting the target is 0.4, respectively the probability of missing is 0.6;
  2. We shot 100 times and needed to calculate the probability that the hits would be between 50 and 70.

We have a standard Bernoulli scheme with two possible outcomes.
We can see that solving this problem using the standard Bernoulli scheme will be very problematic since we will have to go through all the possible probabilities in turn, the probability that we hit 50, times hit 51 times, and so on up to 70. That is why we will use the CLT to solve this task.

Tarea

In the image above, we showed that the value of interest to us can be approximated using a Gaussian distribution with a mean equal to 40 and a variance equal to 24.

Your task is to calculate the required probability: in the first section, we considered that you can use CDF for this. Your task is:

  1. Import norm class from scipy.stats module.
  2. Use .cdf() method of norm class to calculate probability.

Switch to desktopCambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
¿Todo estuvo claro?

¿Cómo podemos mejorarlo?

¡Gracias por tus comentarios!

Sección 2. Capítulo 5
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bookChallenge: Application of the CLT to Solving Real Problem

Let's imagine that we need to solve the following problem:

  1. Suppose that we come to the shooting range and start shooting, the probability of hitting the target is 0.4, respectively the probability of missing is 0.6;
  2. We shot 100 times and needed to calculate the probability that the hits would be between 50 and 70.

We have a standard Bernoulli scheme with two possible outcomes.
We can see that solving this problem using the standard Bernoulli scheme will be very problematic since we will have to go through all the possible probabilities in turn, the probability that we hit 50, times hit 51 times, and so on up to 70. That is why we will use the CLT to solve this task.

Tarea

In the image above, we showed that the value of interest to us can be approximated using a Gaussian distribution with a mean equal to 40 and a variance equal to 24.

Your task is to calculate the required probability: in the first section, we considered that you can use CDF for this. Your task is:

  1. Import norm class from scipy.stats module.
  2. Use .cdf() method of norm class to calculate probability.

Switch to desktopCambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
¿Todo estuvo claro?

¿Cómo podemos mejorarlo?

¡Gracias por tus comentarios!

Sección 2. Capítulo 5
toggle bottom row

bookChallenge: Application of the CLT to Solving Real Problem

Let's imagine that we need to solve the following problem:

  1. Suppose that we come to the shooting range and start shooting, the probability of hitting the target is 0.4, respectively the probability of missing is 0.6;
  2. We shot 100 times and needed to calculate the probability that the hits would be between 50 and 70.

We have a standard Bernoulli scheme with two possible outcomes.
We can see that solving this problem using the standard Bernoulli scheme will be very problematic since we will have to go through all the possible probabilities in turn, the probability that we hit 50, times hit 51 times, and so on up to 70. That is why we will use the CLT to solve this task.

Tarea

In the image above, we showed that the value of interest to us can be approximated using a Gaussian distribution with a mean equal to 40 and a variance equal to 24.

Your task is to calculate the required probability: in the first section, we considered that you can use CDF for this. Your task is:

  1. Import norm class from scipy.stats module.
  2. Use .cdf() method of norm class to calculate probability.

Switch to desktopCambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
¿Todo estuvo claro?

¿Cómo podemos mejorarlo?

¡Gracias por tus comentarios!

Let's imagine that we need to solve the following problem:

  1. Suppose that we come to the shooting range and start shooting, the probability of hitting the target is 0.4, respectively the probability of missing is 0.6;
  2. We shot 100 times and needed to calculate the probability that the hits would be between 50 and 70.

We have a standard Bernoulli scheme with two possible outcomes.
We can see that solving this problem using the standard Bernoulli scheme will be very problematic since we will have to go through all the possible probabilities in turn, the probability that we hit 50, times hit 51 times, and so on up to 70. That is why we will use the CLT to solve this task.

Tarea

In the image above, we showed that the value of interest to us can be approximated using a Gaussian distribution with a mean equal to 40 and a variance equal to 24.

Your task is to calculate the required probability: in the first section, we considered that you can use CDF for this. Your task is:

  1. Import norm class from scipy.stats module.
  2. Use .cdf() method of norm class to calculate probability.

Switch to desktopCambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
Sección 2. Capítulo 5
Switch to desktopCambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
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