Question

Suppose that 2000 points are selected randomly and independently from the unit square {(x,y)| 0<=x<1, 0<=y<1}
Let W equal number of points that fall into A ={(x,y)|x^2+y^2<1}
How W is distributed?
Please, help

Answer 1

to me, n =2000, but how to define p?

Answer 2

Bernoulli distribute need n, p to define W(n, p)

Answer 3

The answer from the book said p =pi/4, but I don't see the logic on it.

Answer 4

this is the whole thing we have, and A occupied > 1/2 of the square whose sides are 1.
How P(A) =pi/4?

Answer 5

@kirbykirby

Answer 6

If A is the region for your event and R is the 2-D region, then \[P(A \in R)=\frac{area ~of ~A}{area~of~R}=\frac{(\pi (1)^2)/4}{1\times 1}\] since the unit square area is 1, and the area of the sector of the circle is 1/4 of the area of the full circle

Answer 7

Oh, I didn't study this formula yet :)

Answer 8

Thanks for the help. May be I will get this formula today.:)

Answer 9

ya it works when you have a uniform distribution over some 2-D region