## Exercises of Probability and Statistics

To obtain the credit for the exercises of the course of Probability and Statistics the students are required to fulfill the following conditions:

- 10 attendances to the practice lectures

- 6 homeworks

- a score greater than or equal to 50% in a written test that will be done during a practice lecture

The homework are assigned every week. The homework must be sent within the midnight of Tuesday before the next practice lecture.

If you are an erasmus student and you can prove that you cannot attend the practice lectures, than you can send an email (within the end of October) to vitali@karlin.mff.cuni.cz and ask to have instead the following requirements to get the credit:

- 8 homeworks

- a score greater than or equal to 50% in a written test that will be done during a practice lecture

Such choice is not changeable.

The **exercises for Christmas holidays** can be found here.
All the exercises must be solve to get the homework point. The deadline for this exercises is the midnight of January 8th, but I thought it could be useful for you to have them before the Zapocet test.

**My personal Christmas gift** for you is an extra Christmas homework that counts as extra point (so that in total you can get 2 points). The assignment is to write a code that computes and shows the following:

1) generate 10000 random numbers from a distribution that you like (declare explicitly which distribution you are considering and declare its expected value and its standard deviation as well)

2) extract a sample of 40 points and compute the sample average

3) given an alpha = 10% compute the confidence interval for the real average using the known standard deviation

4) observe if the real average follows within the constructed interval

5) repeat step 2-5 for a large (>1000) number of times and update each time the proportion of times in which the step 4 is successful (if everything is working well you know to which value the proportion should converge...).

**Here you can find several exercises that cover a large part of the material. This collection is quite extensive but is not fully exhaustive. To prepare for the credit test, please review all the material and the exercises proposed during the practicals.**

**The meeting schedule has been changed. The practicals will be on Wednesday at 7PM in room S5. **

**I sent by email the result of the Zapocet test. If you didn't receive it, please contact me. **