An Introduction to the Binomial Distribution
An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at http://www.statcan.gc.ca/pub/84-537-x/4064441-eng.htm. The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932
Видео An Introduction to the Binomial Distribution канала jbstatistics
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at http://www.statcan.gc.ca/pub/84-537-x/4064441-eng.htm. The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932
Видео An Introduction to the Binomial Distribution канала jbstatistics
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
An Introduction to the Geometric DistributionThe Binomial Distribution and Test, Clearly Explained!!!Binomial Distribution (Introduction) | ExamSolutionsBayes theorem, the geometry of changing beliefsBinomial Probability (1 of 2: Preliminary Example w/ Probability Tree)An Introduction to the Poisson DistributionStatistics 101: The Binomial DistributionBinomial distributions | Probabilities of probabilities, part 1The Binomial Distribution: Crash Course Statistics #15Binomial Distribution EXPLAINED!The Binomial Distribution: Mathematically Deriving the Mean and VarianceExponential Distribution! Definition | Calculations | Why is it called "Exponential"?Statistics Lecture 5.3: A Study of Binomial Probability DistributionsAn Introduction to the Normal DistributionAn Introduction to the Hypergeometric DistributionPoisson Distribution EXPLAINED!Overview of Some Discrete Probability Distributions (Binomial,Geometric,Hypergeometric,Poisson,NegB)The Relationship Between the Binomial and Poisson DistributionsIntroduction to the Multinomial Distribution