Question: Please I need help with this for better understanding and clarity. Thank you. b) A random variable X has an exponential distribution with mean =1/2.

Please I need help with this for better understanding and clarity. Thank you.

Please I need help with this for better understanding and clarity. Thank

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

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