Question: [o-algebra : Properties and Construction]. (a) Show that a o-algebra is also an algebra. (b) Given a sample space N and a o-algebra F

[o-algebra : Properties and Construction]. (a) Show that a o-algebra is also

[o-algebra : Properties and Construction]. (a) Show that a o-algebra is also an algebra. (b) Given a sample space N and a o-algebra F of the subsets of 2, show that if A, B E F, A\B and AAB, the symmetric difference of A and B are present in F. (c) Consider the random experiment of throwing a die. If a statistician is interested in the occurrence of either an odd or an even outcome, construct a sample space and a o-algebra of subsets of this sample space. (d) Let A1, A2, taining A1, A2, .., A,. How many sets are there in F? (Give an upper bound that is attainable under certain conditions). List all the sets in F for n = An be arbitrary subsets of 2. Describe (explicitly) the smallest o-algebra F con-

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