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statistic help

 
 
sonpham
 
Reply Thu 22 Sep, 2011 08:56 am
an experiment consists of choosing a point (x,y) at random from the interior of the circle disk x^2+y^2= 4
a/ find P(X>or = 1/2)
b/ find the probability that a chosen point is closer to the center than to the boundary of the disk
c/ find the marginal distribution of X and Y
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markr
 
  1  
Reply Thu 22 Sep, 2011 06:40 pm
@sonpham,
(a) Through the circle of radius 2 centered at the origin, draw a vertical line at x=0.5. What fraction of the circle's area lies to the right of the line?

(b) The points closer to the center are contained in a circle of radius 1. What's the ratio of the area of the smaller circle to the area of the larger circle?
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raprap
 
  1  
Reply Fri 23 Sep, 2011 04:22 am
@sonpham,
Compare areas.

The probability of a point (x,y) is within the circle of radius 2 with a center at the origin is a certainty.

If x>.5, find the area of the circle segment where x>.5--use markr's recommendation draw a line at x=.5 and find the area of the circle segment above that line. The probability of this condition is the is the ratio of this segment and the area described circle.

Second part would be to find the diameter of a circle that has half the area of the described circle with radius of 2.

Rap
markr
 
  1  
Reply Fri 23 Sep, 2011 01:12 pm
@raprap,
Not so on part (b). The dividing "line" is a circle of radius 1. He needs the probability of landing in the smaller circle.
raprap
 
  1  
Reply Fri 23 Sep, 2011 06:55 pm
@markr,
Correct I misunderstood.

P(E)< the ratio of the areas of two circles with radius 1 and 2.
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