Uploaded June 2012 | Updated September 2026, 2 minutes ago
I work through a few probability examples based on some common discrete probability distributions (binomial, Poisson, hypergeometric, geometric -- but not necessarily in this order). I assume that you've been previously introduced to these distributions (although this isn't necessary for the geometric problem, as the probability is easily calculated from basic probability rules). Students sometimes have difficulty determining the appropriate distribution to use, so this video may give some help with the proper thought process.
I work through a few probability examples based on some common discrete probability distributions (binomial, Poisson, hypergeometric, geometric -- but not necessarily in this order). I assume that you've been previously introduced to these distributions (although this isn't necessary for the geometric problem, as the probability is easily calculated from basic probability rules). Students sometimes have difficulty determining the appropriate distribution to use, so this video may give some help with the proper thought process.




![Intro to Confidence Intervals for One Mean (Sigma Known)
An introduction to confidence intervals for the population mean mu. These methods are appropriate when we are sampling from a normally distributed population, where the population standard deviation sigma is known. When the population standard deviation is not known, as is usually the case, we need to use a slightly different method (a method based on the t distribution).
The 2D:4D ratio data (from the right hand) is simulated data with the same summary statistics as found in:
Stevenson et al. (2007). Attention Deficit/Hyperactivity Disorder (ADHD) Symptoms and Digit Ratios in a College Sample. American Journal of Human Biology. 19:41-50.
For those that use R, here is the R code to find the values given in the video:
To find the value of a standard normal random variable that has an area of 0.025 to the left,
qnorm(.025)
[1] -1.959964
To find the value of a standard normal random variable that has an area of 0.025 to the right,
qnorm(.975)
[1] 1.959964
To find the value of a standard normal random variable that has an area of 0.05 to the left,
qnorm(.05)
[1] -1.644854
To find the value of a standard normal random variable that has an area of 0.05 to the right,
qnorm(.95)
[1] 1.644854 Intro to Confidence Intervals for One Mean (Sigma Known)](https://i.ytimg.com/vi/KG921rfbTDw/mqdefault.jpg)


![An Introduction to the Hypergeometric Distribution
An introduction to the hypergeometric distribution. I briefly discuss the difference between sampling with replacement and sampling without replacement. I describe the conditions required for the hypergeometric distribution to hold, discuss the formula, and work through 2 simple examples.
I also discuss the relationship between the binomial distribution and the hypergeometric distribution, and a rough guideline for when the binomial distribution can be used as a reasonable approximation to the hypergeometric. I finish with a brief example involving the multivariate hypergeometric distribution.
For those using R, here is the R code to find the probabilities for the examples in this video:
The probability of picking exactly 4 red balls when picking 5 balls from a source containing 6 red and 14 yellow.
Without replacement (hypergeometric):
choose(6,4)*choose(14,1)/choose(20,5)
[1] 0.01354489
or
dhyper(4,6,14,5)
[1] 0.01354489
With replacement (binomial):
dbinom(4,5,6/20)
[1] 0.02835
The probability of picking exactly 7 females when randomly sampling from a school with 1100 female and 900 male students.
Without replacement (hypergeometric):
choose(1100,7)*choose(900,3)/choose(2000,10)
[1] 0.1664901
or
dhyper(7,1100,900,10)
[1] 0.1664901
With replacement (binomial):
dbinom(7,10,1100/2000)
[1] 0.1664783
Multivariate hypergeometric, probability of picking exactly 3 Democrats, 2 Republicans, and 1 independent in the sample.
choose(12,3)*choose(24,2)*choose(8,1)/choose(44,6)
[1] 0.06881377
or, with the extraDistr package installed:
dmvrhyper(c(3,2,1),c(12,24,8),6) An Introduction to the Hypergeometric Distribution](https://i.ytimg.com/vi/L2KMttDm3aY/mqdefault.jpg)


