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statistics on PlanetMath

This entry is supposed to become a textbook on statistics - or at least a guide to the statistics-related entries on PlanetMath. It will refer to related entries (e.g. from probability) that are not listed in the same MSC.

(This is currently a stub article. See also Textbook projects on PlanetMath.)

statistics on PlanetMath is owned by John Smith, Joe Corneli, yark.

How to Cite This Entry

John Smith, Joe Corneli, yark. "statistics on PlanetMath" (version 4). PlanetMath.org. Freely available at http://planetmath.org/StatisticsOnPlanetMath.html.

Classification

AMS MSC:

62-01 (Statistics :: Instructional exposition (textbooks, tutorial papers, etc.))

Pending Errata and Addenda

None. [ View all 1 ]

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Discussion

jump to page: 1 2 3 >> of 3 (14 items)

Two statistics questions regarding unbiased estimators by skywalker on 2010-03-18 21:53:43

a) Let X~B(n,p) be a Binomial random variable with n>=2. Let (p^) = X/n be the usual unbiased estimator of the success probability p. Show that (p^)*(1-(p^)) is not an unbiased estimator of p*(1-p), and find a modification of (p^)*(1-(p^)) that is unbiased.

b) Consider a Poisson process with rate lamda>0, for which we observe the number N of events occurring in the time interval (0,1]. Then N has a Poisson(lamda) distribution. Suppose we wish to estimate the probability q=e^(-3*lamda) that no event occurs in the interval (0,3]. Show that the estimator (-2)^N is an unbiased estimator of q. Comment briefly on whether you think that (-2)^N is a good estimator of q.

Can anybody guide me through how to solve these two problems. Details will be much appreciated! I hope with these two problems, I can deal with similar problems in the future. Thanks so much.

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July Ponder This!!!!!!!!!!!!!! by Parashar on 2009-06-30 02:56:12

What is the probability that the last move in a backgammon (link - http://en.wikipedia.org/wiki/Backgammon) game will be a double? To make things easier, we assume that all the 15 checkers of each player are at their 1-point (just ready to bear-off); so each player, in its turn, removes (bear-off) two checkers for every non-double throw and four checkers for every double.

Hint: The solution is *not* the trivial 1/6.

http://en.wikipedia.org/wiki/Backgammon

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Re: July Ponder This!!!!!!!!!!!!!! by dh2718 on 2009-06-30 22:44:26
- Re: July Ponder This!!!!!!!!!!!!!! by Pedro A. Fernandez on 2009-07-01 03:20:50
- - Re: July Ponder This!!!!!!!!!!!!!! by dh2718 on 2009-07-01 06:53:50
  - - Re: July Ponder This!!!!!!!!!!!!!! by Pedro A. Fernandez on 2009-07-01 11:25:27
  - Re: July Ponder This!!!!!!!!!!!!!! by Parashar on 2009-07-06 04:29:55
  - - Re: July Ponder This!!!!!!!!!!!!!! by dh2718 on 2009-07-06 06:59:42
    - - Re: July Ponder This!!!!!!!!!!!!!! by dh2718 on 2009-07-08 07:32:41
      - Re: July Ponder This!!!!!!!!!!!!!! by masadusman on 2009-07-08 17:30:53
        
        Re: July Ponder This!!!!!!!!!!!!!! by masadusman on 2009-07-13 14:37:01

New Year Ponder This!!! by Parashar on 2009-01-04 23:46:02

Consider the following game. You have an opportunity to buy lottery tickets. Each ticket has a value t randomly and independently picked from the continuous and uniform distribution on the interval(0,1). Each ticket costs c (0<c<1). If you don't like the ticket you get you can throw it away and buy another one (at a cost of c). You can do this as often as you want. You can stop at any time and cash in the current ticket at which point the game ends. Your winnings are the value of the ticket you cashed less the cost of all the tickets you bought. You don't have to buy any tickets in which case your winnings are 0. If you adopt the best strategy what are your expected winnings as a function of c?

Suppose we modify the game so that you don't have to throw away any tickets. When you decide to stop buying tickets you can cash in any (but only one) of the tickets you have purchased and the game ends. Now what are your expected winnings (using the best strategy) as a function of c?

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Re: New Year Ponder This!!! by Roger Lipsett on 2009-01-05 21:46:21
- Re: New Year Ponder This!!! by balakrishnan_v on 2009-01-06 08:21:25
- - Re: New Year Ponder This!!! by Parashar on 2009-01-06 23:41:49

Exciting Problem by Parashar on 2008-07-07 05:40:03

There is a very exciting problem at http://projecteuler.net/index.php?section=problems&id=202

Is any one interested in discussing that?

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Re: Exciting Problem by lynx on 2008-07-07 13:55:06
- Re: Exciting Problem by lynx on 2008-07-08 08:57:37
- - Re: Exciting Problem by Parashar on 2008-07-08 23:44:56
  - - Re: Exciting Problem by dh2718 on 2008-07-09 03:39:02
    - - Re: Exciting Problem by Parashar on 2008-07-09 04:50:02
      - Re: Exciting Problem by lynx on 2008-07-09 11:55:01
Re: Exciting Problem by YourInnerNurmo on 2008-07-07 20:36:14
- Re: Exciting Problem by Parashar on 2008-07-08 00:32:22
Re: Exciting Problem by Raymond Puzio on 2008-07-07 23:57:20

grid by Parashar on 2008-06-26 05:31:07

You have a list of items you need to buy today, and you know the locations (represented as points on a cartesian grid) of a few stores in the area. You also know which of these stores are selling each item on your list, and at what price each store sells it. Given the price of gas, what is the minimum amount you need to spend in order to buy all the items on your shopping list and then drive back home? You start and end the journey at your house, which is located at (0,0).

To make matters interesting, some of the items on your list may be perishable. Whenever you make a purchase that includes one or more perishable items, you cannot drive to another store without first stopping back at your house. Every item on your shopping list is guaranteed to be sold by at least one store, so the trip will always be possible.

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statistics on PlanetMath

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Pending Errata and Addenda

Interact

Discussion