S01E04: Count the Pakistani Soldiers

Question:

If you capture 10 random soldiers of an army with ID numbers, given that the ID numbers are serialized how do you estimate the total number of soldiers in the army?

For example, if the 10 captured soldiers had numbers ranging from 109 to 8136, what’s the total count of soldiers in the army?

Additional Questions:

Can we reverse this question? If we are given the population size, can we predict where the random soldiers will be given we pick N random soldiers?

Can the question be changed to a scenario where we are observing random points on a line? If so, where will a random single point be estimated on a unit line over many experiments?

What is this sense of fairness when we are picking things randomly?

If we can estimate the positions of random points when we are given the population, can we estimate the population when we are given the random points?

How will your estimation change if we increase or decrese the number of random points (sample size)?

Coding Assignments:

Create a program to find out where a particular random point will lie when we are generating N random points on a unit line.

Plot the relationship between number of points and average distance between these points.

Create programs to figure out the estimated minimum, estimated maximum, the populations size (range), and other things when we are given some N random points.

Using the simulations and graphs try to come up with a formulas.

← Back to Season 01