Husband and wife with independent heights

Firstly explain the scenario — it is based on clearances under a 2.1 metre high door frame in order to make the diagram on the left clearer.

Click Accumulate then take a few samples.

(Click on any cross to display the corresponding husband and wife.)


The distance from the top of the woman's head to a fixed location (ground or door frame) has lower spread than the distance to a variable location (top of the man's head).


This scenario corresponds to a husband and wife whose heights have independent normal distributions. The husband's height is normal with mean 1.85 metres and the wife's height is normal with mean 1.7 metres. The distributions for both sexes have standard deviation 0.1 metres.

Husband's height in metres is N(1.85, 0.1) and wife's is independent N(1.7, 0.1)

The door frame is 2.1 metres high. The clearances are therefore N(0.25, 0.1) and N(0.4, 0.1).