A random variable X has an exponential distribution with mean = 12. Find: i. [1 MARK]...

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A random variable X has an exponential distribution with mean = 12. Find: i. [1 MARK] [1 MARK] [3 MARKS] [2 MARKS] ii. iii. iv. ii. iii. iv. V. P(X> 3) P(X> 2) P(X> 3| X > 2) Show that P(X> 1) = P(X> 3| X > 2) Consider tossing a fair six-sided die once and define events A = 2, 3), and C= {1, 2, 3, 4). Calculate the following: i. P(A) P(A/B) P(A/C) Are A and B dependent or independent? Explain Are A and C dependent or independent? Explain = {2, 4, 6}, B = {1, [1 MARK] [2 MARKS] [2 MARKS] [1 MARK] [1 MARK] A random variable X has an exponential distribution with mean = 12. Find: i. [1 MARK] [1 MARK] [3 MARKS] [2 MARKS] ii. iii. iv. ii. iii. iv. V. P(X> 3) P(X> 2) P(X> 3| X > 2) Show that P(X> 1) = P(X> 3| X > 2) Consider tossing a fair six-sided die once and define events A = 2, 3), and C= {1, 2, 3, 4). Calculate the following: i. P(A) P(A/B) P(A/C) Are A and B dependent or independent? Explain Are A and C dependent or independent? Explain = {2, 4, 6}, B = {1, [1 MARK] [2 MARKS] [2 MARKS] [1 MARK] [1 MARK]