Språkstatistik HT96:12

Class:   12
Date:    960925
Topic:   Exercise class 4

Exercise class 4

These exercises are supposed to be handed in on Monday September 30. Please give a motivation for all your answers.

1. You are invited to bet on the outcome of a number of coin flips. If the number of heads in a series of coin flips is five or more higher than expected you will win six dollar and otherwise you will loose a dollar. What game will earn you more money: betting on a series on 100 coin flips or betting on a series of 10,000 flips?

2. Repeat exercise 1 but now you will win if the number of heads is five or more percent higher than expected.

3. In a soccer competition the home playing teams have 50% chance of winning, 25% chance on a draw and 25% chance of losing. Winning earns three points, a draw earns one points and losing earns no points. Make a box model for the number of points that a home playing team can obtain.

4. Team A starts this competition with four home games. How many points do you expect A to have after the 4 games? What is the standard error of that expectation?

5. We observe that team A wins all four games and obtains twelve points. Can the difference between this observation and the result of exercise 4 be explained by a chance error? Or should we reject our null hypothesis that team A can be described with the box from exercise 3?

6. A box contains 1,234,567 cards with number two and the same number of cards with number six. Compute the standard deviation of the box.

7. In the study of Pearson which was described in chapter eight 0.04% of the sons was taller than two meters. We select 2500 sons. What is the probability that more than one of them is taller than 2 meters? (number of sons changed 960930)

8. Now we measure the 2500 sons of exercise 7 and we find out that four of them are taller than two meters. What is the probability of this given Pearson's numbers? Does this result mean that his measurements were wrong? (number of sons changed 960930)

9. You play 100 times at a roulette table by betting one dollar on black. What is the probability that you make a profit? (Roulette rules can be found on page 255 and further)

10. Someone describes to you the the ultimate system of winning at roulette:

    You start betting one dollar on black. If you win you have made a profit. If you loose you bet two dollars on black. If you win you have won your dollar back plus an extra one so you have a profit yet again. If you loose you bet eight dollars on black. You keep doubling your bet until you win. In this way you can easily make a lot of money.

    Is this correct? You do not have to give a formal proof of your answer. Some general reasoning will be enough. If you want to compute things you may assume that the chance of winning one bet is 50%.

Each exercise is worth 1 point.