Question: b) If a random variable X distributed as an exponential distribution with parameter 0 = 100 while Y having the probability density function given by

b) If a random variable X distributed as an exponential distribution with parameter 0 = 100 while Y having the probability density function given by 2y f ( y ) = e B y > 0 B 0 , elsewhere i) Determine the joint density function of X and Y (2 marks) ii) Given P = (X + Y) and Q=Y . Determine the joint density function of P and Q using transformation technique. (6 marks) iii) Determine the marginal density of Q . (4 marks)

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