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statistics on PlanetMath (Topic)

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 PrimeFan. [ full author list (2) | owner history (1) ]
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Cross-references: Textbook projects on PlanetMath, PlanetMath, statistics
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This is version 4 of statistics on PlanetMath, born on 2004-11-13, modified 2006-11-27.
Object id is 6474, canonical name is StatisticsOnPlanetMath.
Accessed 11744 times total.

Classification:
AMS MSC: 62-01 (Statistics :: Instructional exposition )
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ponder september 2007 by PARASHAR on 2007-09-06 00:44:16
A cable TV company has two channels of programming that it can offer (at negligible marginal cost) to a large pool of potential customers. Suppose the value (per unit time) of each channel to each potential customer is an independent random variable uniformly distributed on the interval (0,1) and that value is additive (so the value of both channels to the potential customer is the sum of the values of each individual channel). Assume a potential customer will
buy when the (additional) value is greater than the (additional) price.

1. Suppose the company prices each channel independently. What should it charge for each channel (to maximize revenue) and what will its expected revenue be (per potential customer per unit time)?

2. Suppose the company bundles the channels together so the potential customer has to buy both or neither. What should it charge (to maximize revenue) for the bundle and what will its expected revenue be (per potential customer per unit time)?

Define the consumer surplus to be the difference (assuming it is positive) between what a potential buyer would have been willing to pay for an item and the actual price. If the difference is negative the sale will not take place and the consumer surplus is defined to be 0.

3. What is the consumer surplus (per potential customer per unit time) assuming the cable company prices to maximize revenue for cases 1 and 2 above?


[ reply | up ]
Game by PARASHAR on 2007-06-04 22:16:32
You are playing a game in which you can ask for numbers. Each such number is a random value uniformly (and independently) distributed between 0 and 1. After you receive each number you can decide whether to request an additional number or to stop. When you stop your score is the sum of all the numbers you have received. Let 0<x<1. We ask two questions.


1. Suppose you are trying to achieve a score between x and 1. What are your chances of success?
2. Suppose you are trying to achieve a score between n+x and n+1. What are your chances of success in the limit as n --> infinity?
[ reply | up ]
  • Re: Game by Wkbj79 on 2007-06-04 23:08:36
  • Re: Game by PARASHAR on 2007-06-05 23:21:41
    • Re: Game by PARASHAR on 2007-06-12 07:07:21
      • Re: Game by PARASHAR on 2007-06-14 01:46:58
too popular? by jac on 2006-11-27 20:15:01

This is version 4 of statistics on PlanetMath, born on 2004-11-13, modified 2006-11-27.
Object id is 6474, canonical name is StatisticsOnPlanetMath.
Accessed 1316 times total.

Why so many times accessed and still no major revisions?
[ reply | up ]

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