# 12: Poisson

Poisson |

Title text: Poisson distributions have no value over negative numbers |

## Explanation

In this comic, Cueball expresses himself as a Poisson distribution.

Per Wikipedia, in mathematics, a Poisson distribution is a distribution that shows the probability of a given number of events occurring in a fixed interval of time or space. The horizontal axis typically represents the “number of events” while the vertical axis is a decimal representing the probability (i.e. 0.5 for 50% probability) a given number of events will occur in that fixed interval of time or space. It is commonly represented by a bar graph, or a point graph (sometimes with a line connection to show a trend, even though there is no actual value for non-integers).

A simple example is the number of heads coming up on a fair coin flip. The distribution for one coin flip should be 0.5 at 0 heads and 0.5 at 1 heads; for 2 coin flips, the distribution would be 0.25 at 0 heads, 0.5 at 1 heads and 0.25 at 2 heads; Etc. Multiple graphs like this are sometimes overlaid on one graph with a legend to distinguish the points (one coin flip in red, two coin flips in blue, etc).

What's important to note for this comic is that this distribution only has data points on non-negative integers and is not continuous through decimal numbers or (as the image text tells us) negative numbers because events can’t occur 0.3 of a time, or -2 times.

After implying that the concept of a person being a mathematical distribution is irrational, Black Hat suggests he is “less than zero”. Since the Poisson Distribution doesn’t exist or has no value at negative values, Cueball either leaves or disappears magically.

Hence, the punchline is the same as the title text: Cueball doesn't exist to Black Hat anymore, because he has a value less than zero.

## Trivia

- This is the first appearance of Black Hat in xkcd.
- Randall was still experimenting with character design, as Cueball has a face in the first two frames.

## Transcript

- [Cueball talking to Black Hat]
- Cueball: I'm a poisson distribution!

- Cueball: Still a poisson distribution.
- Black Hat: What the hell, man. Why do you keep saying that?

- Cueball: Because I'm totally a poisson distribution.
- Black Hat: I'm less than zero.

- [Cueball is gone; Black Hat is whistling.]

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# Discussion

Rikthoff (talk) The date of issue of this comic is off. Does anybody have the correct date? Does anybody know the song that BlackHat is singing in the last frame?

I always imagine the song is either the Bangles cover of "hazy shade of winter" from the movie Less than Zero though I have also imagined it to be "saved by zero" by the Fixx.

- Did anyone notice the pun on poison and Poisson? 108.162.254.174 18:39, 10 March 2014 (UTC)

Note that the 'h' in the word 'hell' looks like 'λ'. 141.101.64.35 20:03, 21 July 2014 (UTC)

Also note that the Poisson distribution is "memoryless" (like the exponential distribution) which explains why the Poisson is content to continue repeating this fact. 108.162.222.178 16:44, 21 April 2015 (UTC)

The coinflip distribution described in the second paragraph not a Poisson Distribution. Rather it is a binomial distribution (or a Bernoulli distribution for the single flip case). 108.162.229.163 11:11, 7 September 2015 (UTC)

- I deleted it. 173.245.50.154 12:25, 7 September 2015 (UTC)