Point Estimation help

• Nov 20th 2008, 07:59 PM
isuckatprobability
Point Estimation help
During each lecture in a statistics class, let X equal the number of times that Professor Tanis collides with a computer table at the front of the classroom. Assume that the distribution of X is Poisson with a mean (lambda).

(a) Given n observations of X, find the method of moments estimate of (lambda)
(b) Give a point estimate of (lambda) using the following 11 observations of X that were collected by Chris:

1,0,1,3,3,0,2,2,4,1,1

I could use some direction with this problem....I keep looking through this put together book my professor is constructing with no luck on how to even go about starting to solve this problem.
• Nov 20th 2008, 08:51 PM
mr fantastic
Quote:

Originally Posted by isuckatprobability
During each lecture in a statistics class, let X equal the number of times that Professor Tanis collides with a computer table at the front of the classroom. Assume that the distribution of X is Poisson with a mean (lambda).

(a) Given n observations of X, find the method of moments estimate of (lambda)
(b) Give a point estimate of (lambda) using the following 11 observations of X that were collected by Chris:

1,0,1,3,3,0,2,2,4,1,1

I could use some direction with this problem....I keep looking through this put together book my professor is constructing with no luck on how to even go about starting to solve this problem.

In this question, the Method of Moments says that the mean of the n observations is assumed to be a reasonable estimate for the mean of X ....
• Nov 20th 2008, 09:08 PM
isuckatprobability
for the first part I think I might have gotten it right..I used n = 18, lambda = 1/18*[0(1)+1(0)+2(1)+3(3)+4(3)+5(0)+6(2)+7(2)+8(4)+9(1)+ 10(1)] = 5.55 not sure if I did it right though
• Nov 20th 2008, 09:12 PM
mr fantastic
Quote:

Originally Posted by isuckatprobability
for the first part I think I might have gotten it right..I used n = 18, lambda = 1/18*[0(1)+1(0)+2(1)+3(3)+4(3)+5(0)+6(2)+7(2)+8(4)+9(1)+ 10(1)] = 5.55 not sure if I did it right though

Where has this data come from if n = 18 .......? Be that as it may, it's not difficult to calculate the mean value of a set of data. And that's all you have to do in this question ....
• Nov 20th 2008, 09:13 PM
CaptainBlack
Quote:

Originally Posted by isuckatprobability
for the first part I think I might have gotten it right..I used n = 18, lambda = 1/18*[0(1)+1(0)+2(1)+3(3)+4(3)+5(0)+6(2)+7(2)+8(4)+9(1)+ 10(1)] = 5.55 not sure if I did it right though

It can't be right as the mean should not be larger than any of the observations.

You have 18 collisions in 11 observations, the mean is 18/11

CB
• Nov 20th 2008, 09:34 PM
isuckatprobability
I thought the total # of observations was 18. I found an example that shows them using the equation sum(xi)/n for a poisson distribution...
• Nov 20th 2008, 09:37 PM
isuckatprobability
forget it...I think that equation is for point estimation for lambda...I think you may be correct for part a