(a) Give an example of a random experiment, where the number of members in the sample space is 3. (b) Using Venn diagram show that (AUB) = AC B, where AC = complement of A. (c) Give a combinatorial explanation of the identity (15 H-H (d) Let A, B and C be three events. Find expression for the event so that of A, B and C at most two of them occur. (e) For a finite set A, let N(A) be the number of elements in A. Show that N (AB) = N(A) + N (B) -N(AUB). (f) Let A1, A2, 8 , Ag be independent events so that P (A)=q, 0 0, P (A)>P(B) and P(A|C) P(B|C). (i) Define a random variable. (j) Give an example of a random variable for which P (X 0, P(X>5) > 0 and P(X 2) + P(X2) = 1. (k) Let f be a probability density function such that f(x)=C{e +ex} if x>0 Find C. =0 otherwise, where C is a constant. (1) Give an example of a non-degenerate random variable X, where E (X-4)= E(4-X). (m) If P(X=7)=1, find variance of X. (n) Give an example of a cumulative distribution function F for which lim (F(1)-F(1-h)} = 3. (0) Define a measure of skewness using quartiles.