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.

one of each metals

step-by-step explanation:

boxplot

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)