3
votes
1answer
81 views

Circular distribution of circles

Suppose you have $n$ objects , distributed randomly, in a circular manner of radius $r$. Each objects is of area $A$. So my question is if you draw line everywhere from the center to the surface of ...
0
votes
0answers
11 views

Probability of error in two dimensional signal space

The likelihood decision rule for two dimensional signal space is $r_2$ > $r_1$ for $H_1$ hypothesis and $r_2$ < $r_1$ for $H_0$ hypothesis. The range of $R=[r_1~r_2]$ is $-\infty<r_1<\infty$ ...
0
votes
0answers
77 views

Spatial distribution of bees

* Please please help! I still get stuck. We have a forest for bees, consisting of $4$ non-overlapping regions. $80\%$ of the bees seek honey in the forest while $20\%$ of the bees do so outside the ...
5
votes
2answers
93 views

finding the number of circles we get when randomly placing given patterns into a grid of squares

We have an 11$\times$11 table of squares (consist of 121 squares of dimension 1$\times$1). we have 3 tiles shown in the picture. Each tile has dimension 1$\times$1. we now randomly pick 3 tiles into ...
3
votes
1answer
151 views

Truchet tiles on a flattened cube

We randomly place copies of the tiles into faces of the flattened cube. 1.Find the probability that the circular arcs on the Truchet tiles will form one loop, two loops, three loops and four loops? ...
1
vote
1answer
74 views

A modified Buffon's needle

A needle 2.5cm long is dropped on a piece of paper that has a very fine parallel lines 2.25cm apart drawn on it. What is the probability that the needle lies between the two lines? I can see how ...
8
votes
2answers
338 views

What's the probability that three points determine an acute triangle?

Three distinct points are chosen at random from the unit square. The goal is to find the probability that they form an acute triangle. I started working on this because I want to know how to approach ...