Let N1 and N2 represent the numbers of claims submitted to a life insurance company in April and May, respectively. The joint probability function of N1 and N2 is ( ) 1 2 1 1 1 1 1 2 1 2 3 1 1 , 1, 2,3,..., 1, 2,3,... (, ) 4 4 0, otherwise. n n n n ee n n pn n − − − −       − == =      Calculate the expected number of claims that will be submitted to the company in May, given that exactly 2 claims were submitted in April.

Match the vocabulary to the proper definition. in probability, two events in which 1. conditional probability the outcome of one event is independent of the outcome of a second event. 2. dependent events in probability, two events in which the outcome of one event is dependent on the outcome of a second event. the probability of an event in which the outcome of the event is conditional on the outcome of one or more different events. 3. independent events