Consider the following collective risk model: (i) The claim count random variable N is Poisson with mean 3. (ii) The severity random variable has the following probability (mass) function: Px (1) = 0.6, px (2) = 0.4. (iii) As usual, individual loss random variables are mutually independent and independent of N. Assume that an insurance covers aggregate losses subject to a deductible d = 3. Find the expected value of aggregate payments for this insurance.

A sample of size 26 will be drawn from a population with mean 5 and standard deviation 4.

(a) In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of 5 mm and standard deviation of 0.1 mm. If a rod is selected at random, what is the probability that its diameter will be: (i) less than 4.85 mm; (ii) between 4.9 mm and 5.1 mm? (b) A telephone exchange receives an average of 5 calls per minute. Calculate the probability that, in a given minute, the exchange receives: (i) exactly 5 calls; (ii) 2 calls or fewer.

(A), (B) and (C). Please!

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 35 and standard deviation ? = 11. Find the following probabilities. (Round your answers to four decimal places.)   (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 39 and standard deviation σ = 13. Find the following probabilities. (Round your answers to four decimal places.) (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

3(ii) A bank sets up a Special Purpose Vehicle (SPV) for a CDO issue. The SPV wants to understand the risks that they may face, so they run simulations of the annual cash flows out of their portfolio. Selected results of the simulation are shown in the table below. Annual Portfolio Cash Flows Mean Std. Dev. Min. 5th 10th Percentiles 15th 85th 90th (1,172) 16,651 (7,760) (6,800) (4,880) (3,920) 2,480 95th Max. 14,320 15,280 26,400 The SPV wants to hold risk capital to cover its losses to the 95th percentile, and expected CDO payouts for the next five years add up to $100m. How much capital would you advise them to hold, and why?

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 35 and standard deviation ? = 10. Find the following probabilities. (Round your answers to four decimal places.)   (a) x is less than 60 (b) x is greater than 16 (c) x is between 16 and 60 (d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)