Poisson Distribution in R | R Tutorial 3.2 | MarinStatsLectures

MarinStatsLectures-R Programming & Statistics
25 Aug 201304:01
EducationalLearning
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TLDRIn this educational video, Mike Marin explains how to calculate probabilities for a Poisson random variable using R programming language. With a focus on a variable with a rate of lambda equals 7, he demonstrates the use of 'dpois' for exact probabilities and 'ppois' for cumulative probabilities. He also introduces 'rpois' for random sampling and 'qpois' for quantiles, offering insights into Poisson distribution analysis.

Takeaways
  • 📚 The video is about calculating probabilities for a Poisson random variable using R programming language.
  • 📉 The Poisson distribution has a known rate, denoted as lambda, which in this video is set to 7.
  • 🔢 The 'dpois' command in R is used to find the probability density function values for a Poisson random variable.
  • 🎯 To find the probability of exactly 4 occurrences, the 'dpois' command is used with lambda set to 7, resulting in approximately a 9.1% chance.
  • 📈 The 'dpois' command can return multiple probabilities for different values of X, from 0 to 4 in the given example.
  • 🔍 To find the cumulative probability of X being less than or equal to a certain value, one can sum the individual probabilities or use the 'ppois' command.
  • 📊 The 'ppois' command is used to calculate the cumulative distribution function (CDF) for the Poisson distribution, providing probabilities of 'less than or equal to' a value.
  • 🔄 The 'ppois' command can also be used to find the upper tail probability by setting the 'lower.tail' parameter to FALSE.
  • 🔮 The 'rpois' command is used to generate random samples from a Poisson distribution.
  • 📐 The 'qpois' command is used to find the quantiles for a Poisson distribution.
  • 👨‍🏫 The video also suggests checking out another video on the normal distribution for additional insights into using these commands.
Q & A

  • What is the topic of the video presented by Mike Marin?

    -The video is about calculating probabilities for a Poisson random variable using the R programming language.

  • What is the known rate (lambda) for the Poisson distribution discussed in the video?

    -The known rate (lambda) for the Poisson distribution in the video is 7.

  • Which R commands are mentioned in the video for calculating Poisson probabilities?

    -The video mentions 'ppois' and 'dpois' commands for calculating Poisson probabilities.

  • How can one access help for the 'dpois' command in R?

    -To access help for the 'dpois' command, one can type 'help(dpois)' or use '?dpois' in the R console.

  • What does the 'dpois' command calculate in the context of the video?

    -The 'dpois' command calculates the probability density function values for a Poisson random variable.

  • What is the probability of exactly 4 occurrences for a Poisson random variable with lambda equal to 7?

    -The probability of exactly 4 occurrences for a Poisson random variable with lambda equal to 7 is approximately 9.1 percent.

  • How can one calculate the probability of multiple occurrences for a Poisson random variable?

    -One can use the 'dpois' command in R to calculate the probability of multiple occurrences by specifying different values of X from 0 up to the desired number.

  • What is another way to calculate the probability that X is less than or equal to 4, besides summing the individual probabilities?

    -Another way to calculate the probability that X is less than or equal to 4 is by using the 'ppois' command with the lower tail set to TRUE.

  • How can one find the probability that X is greater than or equal to a certain value using R?

    -To find the probability that X is greater than or equal to a certain value, one can use the 'ppois' command with the lower tail set to FALSE.

  • What R command can be used to take a random sample from a Poisson distribution?

    -The 'rpois' command can be used to take a random sample from a Poisson distribution.

  • What command in R is used to find quantiles for the Poisson distribution?

    -The 'qpois' command is used in R to find quantiles for the Poisson distribution.

  • What additional resource is recommended for further insights on using these commands?

    -Mike Marin recommends watching his video on the normal distribution for further insights on how to use these commands.

Outlines
00:00
📚 Introduction to Poisson Distribution in R

In this introductory paragraph, Mike Marin presents the topic of the video, which is calculating probabilities for a Poisson random variable using the R programming language. The video will focus on a Poisson distribution with a known rate of lambda equals 7. Mike introduces the 'ppois' and 'dpois' commands in R for calculating probabilities and accessing help for these commands. He demonstrates how to use 'dpois' to find the probability of exactly 4 occurrences, showing that there is approximately a 9.1% chance of this event. The paragraph also explains how to obtain multiple probabilities for occurrences ranging from 0 to 4 using the same command.

Mindmap
Keywords
💡Poisson Random Variable
A Poisson random variable is a type of discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. In the video's context, it is the subject of the tutorial, with the variable following a Poisson distribution characterized by a known rate, lambda.
💡Lambda (λ)
Lambda, represented by the Greek letter λ, is the rate parameter of the Poisson distribution, indicating the average number of events occurring in a given time frame. In the script, lambda is set to 7, which is the average number of occurrences the random variable is expected to have.
💡ppois Command
The 'ppois' command in R is used to calculate the cumulative distribution function (CDF) for a Poisson distribution. It provides the probability that a Poisson random variable is less than or equal to a certain value. In the video, 'ppois' is used to find the probability of the random variable being less than or equal to 4.
💡dpois Command
The 'dpois' command in R is utilized to calculate the probability mass function (PMF) for a Poisson distribution. It gives the probability of a Poisson random variable being exactly equal to a specified value. The script demonstrates using 'dpois' to find the probability of exactly 4 occurrences.
💡Probability Density Function (PDF)
In the context of probability theory, the probability density function is a function that describes the likelihood of a continuous random variable taking on a particular value. For discrete distributions like Poisson, it's referred to as the probability mass function. The script uses 'dpois' to find values for the PDF of the Poisson distribution.
💡Cumulative Distribution Function (CDF)
The cumulative distribution function, or CDF, is the probability that a random variable takes a value less than or equal to a certain value. In the script, the 'ppois' command is used to calculate the CDF for the Poisson distribution to find the probability of the variable being less than or equal to a given number.
💡Help Menu
The Help menu in R is a resource for users to get assistance on commands and functions. The script mentions accessing the Help menu by typing 'help' followed by the command name in brackets or by using a question mark in front of the command name to get information on how to use 'ppois' and 'dpois'.
💡Sum Command
The 'sum' command in R is used to add up a series of numbers or elements. In the video script, it is suggested as a method to calculate the total probability by summing individual probabilities calculated by 'dpois' for different values of the Poisson random variable.
💡Lower Tail
In probability distributions, the lower tail refers to the probability of a random variable being less than or equal to a certain value. The script explains using the 'ppois' command with the lower tail set to TRUE to find the probability of the Poisson variable being less than or equal to 4.
💡Upper Tail
The upper tail in a probability distribution is the probability of a random variable being greater than a certain value. The script describes using the 'ppois' command with the lower tail set to FALSE to calculate the probability of the Poisson variable being greater than or equal to 12.
💡rpois Command
The 'rpois' command in R is used to generate random samples from a Poisson distribution. It is mentioned in the script as a way to take a random sample from the distribution defined by the given lambda value.
💡qpois Command
The 'qpois' command in R is used to find the quantiles of a Poisson distribution. Quantiles are the values below which a certain percentage of the data falls. The script briefly mentions 'qpois' as a command to find quantiles for the Poisson distribution.
Highlights

Introduction to calculating probabilities for a Poisson random variable in R.

Focus on a Poisson distribution with a known rate lambda equal to 7.

Explanation of using 'ppois' and 'dpois' commands for Poisson probabilities.

How to access help for R commands using 'help' or '?'.

Using 'dpois' to find the probability density function for a given X.

Calculating the probability of exactly 4 occurrences with lambda = 7.

Approximately 9.1 percent chance of exactly 4 occurrences.

Returning multiple probabilities using 'dpois' for X from 0 to 4.

Visualizing probabilities of 0 to 4 occurrences with 'dpois'.

Summing probabilities to find P(X ≤ 4) using 'sum' command.

Using 'ppois' to find cumulative probabilities with lower tail probabilities.

Calculating P(X > 12) with 'ppois' for upper tail probabilities.

Using 'rpois' for random sampling from a Poisson distribution.

Using 'qpois' to find quantiles for the Poisson distribution.

Recommendation to watch the video on the normal distribution for related insights.

Closing remarks and invitation to watch other instructional videos.

Transcripts

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