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Consider subset X of exercise 1 again. Is X an o-algebra? Reason!

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

exercise sheet 2

All submissions are to be labeled with the name, matriculation number and number of the exercise group on the top right edge.

Always give a complete calculation method and a comprehensible justification for your solutions. For tasks with R, the input and the output together with the explanation must be submitted.

Exercise 3: (2 points) Consider subset X of exercise 1 again. Is X an o-algebra? Reason!

Exercise 4: (4 points) The eight faces of a regular octahedron1 are labeled with the numbers 1, 2,..., 8.

(a) Describe the random experiment "simple throw of the octahedron>when thrown, the octahedron shows the color green" as a subset of the basic set. What is the probability of this event?

(c) What is the probability of rolling an even number with a blue color?

(d) What is the probability of rolling an even number or a blue number?

Task 5: (3 points) Amalia, Berenice, Carlotta, Dorothea and Edeltraud are good friends. The five friends choose two of themselves to buy ice cream. What are the possibilities? The results are therefore two-element sets, such as {Berenice, Edeltraud}. The selection is random, and the random experiment can be described as a Laplace experiment. Describe the event »Carlotta is elected, but not Amalia«< as a subset of the basic set and determine its probability.

 

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