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.

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?