Uploaded March 2024 | Updated September 2026, 2 hours ago
Not even close. Lots of this sort of stuff in textbooks as well. WT...H?
(And just in case anybody thinks that I think I'm in that far right tail --- I'm definitely the midwit here.)
For the normal distribution, the ratio of area between 0 and 1 SD from the mean to that of the area between 1 and 2 SD from the mean is about 2.51. With rounding, the figure states it as 34/14, which is about 2.43. The ratio of the actual areas seen in this plot is about 3.75 (50% larger than it should be). Not even close.
Not even close. Lots of this sort of stuff in textbooks as well. WT...H?
(And just in case anybody thinks that I think I'm in that far right tail --- I'm definitely the midwit here.)
For the normal distribution, the ratio of area between 0 and 1 SD from the mean to that of the area between 1 and 2 SD from the mean is about 2.51. With rounding, the figure states it as 34/14, which is about 2.43. The ratio of the actual areas seen in this plot is about 3.75 (50% larger than it should be). Not even close.









![An Introduction to the Geometric Distribution
An introduction to the geometric distribution. I discuss the underlying assumptions that result in a geometric distribution, the formula, and the mean and variance of the distribution. I work through an example of the calculations and then discuss the cumulative distribution function.
For those using R, here is the R code for the example in this video:
NB R uses a different definition of the random variable than I do here. I define the random variable X to be the number of trials required to get the first success. R defines the random variable to be the number of *failures* before getting the first success (lets call this Y). Then Y = X - 1, and well have to make this adjustment when using dgeom, pgeom, or rgeom. Some might find this confusing, and if you do, dont use these functions.
Sampling from a large population where 30% have CPR training until we get the first person with CPR training.
Finding the probability that it happens on the sixth person sampled:
(.3)*(.7)^5
[1] 0.050421
or
dgeom(6-1,.3)
[1] 0.050421
Finding the probability that it happens on or before the third person sampled:
.3+.3*.7+.3*.7^2
[1] 0.657
or
1-.7^3
[1] 0.657
or
pgeom(3-1,.3)
[1] 0.657 An Introduction to the Geometric Distribution](https://i.ytimg.com/vi/zq9Oz82iHf0/mqdefault.jpg)