An Open Probability Question
A random probability question I was pondering mid a stagnant lecture today. I’ll be considering it later, but don’t have the chops to deal with it right now.
Algorithm
input whole number t representing a number of iterations
Draw a node at (0,0)
i=0
While i<t:
For all nodes:
Choose an angle at random
Draw an edge of length 1-(te) where e is an arbitrarily small value
Draw a node at that location
[end for]
i=i+1
[end while]
[end algorithm]
Question 01: Given a whole number t, what is the probability that no two drawn edges intersect and that no two nodes overlap? What is the expected number of such co-incisions?
Modified Algorithm
input whole number t representing a number of iterations
Draw a node at (0,0)
i=0
While i<t:
For all leaves:
Choose an angle at random
Draw an edge of length 1-(te) where e is an arbitrarily small value
Draw a node at that location
Choose an angle at random
Draw an edge of length 1-(te) where e is an arbitrarily small value
Draw a node at that location
[end for]
i=i+1
[end while]
[end algorithm]
Question 02: Repeat Question 01 with the new algorithm.
