Claims are reported to a car insurance company according to a Poisson process with an average of 5 claims per day. The USD amount of each claim follows an exponential distribution with mean $2,000. Suppose that all claims and the total number of reported claims are independent of each other. (a) Compute the expected total sum of claims (i. e., the total USD amount) after one week. (b) Find the probability that more than one claim with claim size $10,000 or higher will be reported to the insurance company within one week.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)