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.

468

step-by-step explanation:

positive

step-by-step explanation:

the quadrant is facing upwards

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.