MATH3280-2020-QUiz1

Quiz 1 MATH 3280 3.00 Page 2 of 2 Question 1 Let the random variables (RVs) N ∈ N and M ∈ N denote the number of claims submitted to a life insurer in April and May, , respectively. . The joint probability mass function (PMF) of the two RVs is given by p ( n, m ) = 3 4 ( 1 4 ) n - 1 e - n (1 - e - n ) m - 1 , n, m = 1 , 2 , . . . 0 , otherwise Compute the expected number of claims that the insurer is going to get in May, given that exactly 2 claims were submitted in April. Question 2 Let the RV T ( x ) , x ∈ R + ∪ { 0 } be distributed exponentially with E [ T ( x )] = 3. Com- pute E [ T ( x : 2 )]. (Recall that the last survivor life status ( x : y ) , x, y ∈ R + ∪ { 0 } dies upon the last death of ( x ) and ( y ). The End.