S01E03: The Blindfold Dart Shots
Question:
A shooter fires 100 shots at a circular target (radius 1 unit). None of the shots are perfect, i.e. they all land randomly within the circle. The goal is to find the expected minimum distance from the center across multiple experiments. In simple terms: what will be the estimated closest shot to the center if we throw 100 darts or shoot 100 bullets and all shots land inside the target area, but randomly?
Additional Questions:
How will changing the number of bullets shot at the target change things?
What is the effect of number of experiments we conduct for getting the estimation?
What is the relationship between the number of shots fired and number of experiments ran?
Is there a 2D version of this problem, i.e. can we solve a simpler version of this problem first?
How is the 2D version of this problem different from the 3D version (shooting at a circular target) of this problem?
Coding Assignments:
Create a simulation of this problem in python and try to observe the estimated minimum distance emperically.
Plot graph over multiple experiments and vary the number of shots at the target.
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