The random variables introduced in the previous assignment are both realized 100 times.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Statistics

Please write down every essential calculation and step of your solution.

Every assignment is worth six point.

1. The random variable X is distributed as N(3, 42) and random variable Y is distributed as N(0, 12). The random variables are uncorrelated. Calculate:

a) X + Y

b) X – Y

c) 5X + 6Y

2. The random variables introduced in the previous assignment are both realized 100 times. The estimated (rounded) sample mean and sample standard deviation are exactly the same as expressed previously. Form corresponding mean estimators for both random variables, and calculate the sum (+) and the difference (-) between the two estimators.

3. Explain BRIEFLY, what ”median” is, and why it cannot be calculated for nominal variables.

4. Let’s assume, we have a biased coin, and the probability of tails is 0.3. What is the probability that…

a) …we get eight tails by tossing the coin eight times?

b) …we get two heads by tossing the coin two times?

5. Let’s assume, we have a sample with 100 observation: Integers from 1 to 100 (i.e. 1, 2, …, 100).

Calculate 95% confidence interval for the sample mean.

6. A baker claims that he bakes on average baguettes having length of 0.5 meters. For one month we measure the baguettes baked by him. The sample size is 1000 baguettes, the sample mean is 0.35 meters and the sample standard deviation is 0.1 meters. Test with 5% risk level, if the baker was telling the truth in the first place.

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