Let A be an event that is independent of itself. Which values can P(A) take?

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Exercise 9: (1 point) Let A be an event that is independent of itself. Which values can P(A) take?

Exercise 10: (4 points) Consider the continuous uniform distribution on [0, 1]. Find three subsets A, B, C C[0, 1] which are pairwise independent but not independent.

Exercise 11: (3 points) Consider the regular octahedron from exercise 4 again. The color of the area is considered as a random variable X. Give the mapping rule X and the state set Z. Check if X is really a random variable. Determine the distribution of X.

Exercise 12: (4 points) The three random variables X1, X2, X3 are independent. For k = {1,2,3} let the distribution X be Ber(11).

(a) Determine P([X1 = 1, X2 = 1, X3 = 1]).

(b) Which values can the random variable M = max{X1, X2, X3} assume? Determine the distribution of M

(c) Which values can the random variable S = X1 + X2 + X3 take? Determine the distribution of S

 

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