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Probability Theory Basics
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Probability Theory Basics

Probability Theory Basics

1. Basic Concepts of Probability Theory
Stochastic Experiment and Random EventProbability and It's PropertiesGeometrical ProbabilityChallenge: Solving the Task Using Geometric ProbabilityIndependence and Incompatibility of Random EventsConditional Probability
2. Probability of Complex Events
Inclusion-Exclusion PrincipleChallenge: Solving the Task Using Inclusion-Exclusion PrincipleThe Multiplication Rule of ProbabilityLaw of Total ProbabilityBayes' TheoremChallenge: Solving the Task Using Bayes' Theorem
3. Commonly Used Discrete Distributions
Binomial DistributionChallenge: Solving Task Using Binomial DistributionMultinomial DistributionGeometric DistributionPoisson DistributionChallenge: Solving Task Using Poisson Distribution
4. Commonly Used Continuous Distributions
Continuous Uniform DistributionExponential DistributionChallenge: Solving Task Using Exponential DistributionGaussian DistributionChallenge: Solving Task Using Gaussian Distribution
5. Covariance and Correlation
What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

Challenge: Solving Task Using Gaussian Distribution

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 4. Capítulo 5
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Challenge: Solving Task Using Gaussian Distribution

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 4. Capítulo 5
toggle bottom row

Challenge: Solving Task Using Gaussian Distribution

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Tarea

Suppose you are going fishing.
One type of fish is well caught at atmospheric pressure from 740 to 760 mm Hg.
Fish of the second species is well caught at a pressure of 750 to 770 mm Hg.

Calculate the probability that the fishing will be successful if the atmospheric pressure is Gaussian distributed with a mean of 760 mm and a mean deviation of 15 mm.

You have to:

  1. Calculate the probability that pressure is in the [740, 760] range.
  2. Calculate the probability that pressure is in the [750, 770] range.
  3. As our events intersect, we must use the inclusive-exclusive principle. Calculate the probability that pressure falls into the intersection of corresponding intervals.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
Sección 4. Capítulo 5
Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
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