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### Stock Market Scam

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Date: 02/08/2001 at 11:28:19
From: Amy Gray
Subject: Statistics

One Monday morning you receive in the mail a letter from a firm with
which you are not familiar, stating that the firm sells forecasts
about the stock market for very high fees. To indicate the firm's
ability in forecasting, it predicts that a particular stock, or a
particular portfolio of stocks, will rise in value during the coming
week. The prediction proves to be correct. This routine continues for
seven weeks: Every Monday morning you receive a prediction in the
mail from the firm, and each of these seven predictions proves to be
correct.

On the eighth Monday morning you receive another letter from the firm.
This letter states that for a large fee the firm will provide another
prediction, on the basis of which you can presumably make a large
amount of money on the stock market.

Since you have taken a course in probability and statistics, you
reject this letter. Why? How might this scheme work? If the cost of
printing and postage is \$0.50 per letter, and the "firm" expects the
rate of ignorance of basic probabilistic principles within the US
population to be 10% and to your knowledge stock market predictions
are correct 50% of the time, how large should the "fee" be so that it
breaks even (given your implementation)? (You do not need to factor
in costs of bribing law enforcement or SEC officials, maintaining
offshore accounts, retaining a "fee collection agency," etc.)
```

```
Date: 02/08/2001 at 14:35:12
From: Doctor Shawn
Subject: Re: Statistics

Amy,

Funny how real problems and stat problems sometimes coincide, isn't
it? The SEC gets scams like this all the time. Since you just quote
the problem, I don't know where it's giving you trouble, so I'll just
throw in a little bit to get you started:

Suppose that I start with a pool of, say, 16,384 people. To half of
them I then send out letters predicting that a given stock will rise;
to the other half I send out the same letter, predicting that it will
fall. Since the stock must either rise or fall, 8,192 people will get
a letter with good investment advice. For those 8,192, I then send
out two more sets of letters the next week with more advice. (The
people to whom I gave bad information I just ignore.) And so on, and
so on, for seven weeks. At the end, how many people got seven weeks
of good advice? I can expect 10% of those people to pay up. How much
postage is that? Can you take it from here?

Hope that helps! Feel free to write back with any other questions you

- Doctor Shawn, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability
High School Statistics

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