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Answer the following parts separately:
(a) Suppose that the initial surplus is 10. How large should the adjustment coefficient R be, to ensure that the probability of ruin will be less than 0.10?
(b) Suppose that the adjustment coefficient R = 2/9, λ = 5, and X is exponentially distributed with mean 3. Find c.
(c) You are given that c = 20, λ = 5. All you know about X is that E(X) = 3. What is the probability that the surplus will eventually drop below its initial value?
(d) Suppose that X takes some fixed value with certainty. Show that if the initial surplus does drop below its initial value, the amount of deficit the first time this occurs will be uniformly distributed.
Suppose a shock causes a unit damage to the machine with probability 0.1 and no damage with probability of 0.9. Successive shocks are independent. Suppose the damages are cumulative and the machine can withstand at most four units of damage
A guy wire to the top of a tower makes an angle of 63 degrees with the level ground. At a point 34 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 22 degrees. What is..
In examining the interview results, you find that each customer is listed in a row and each column contains data on: The customer's gender. If you need this data, use the coding convention: 0 for female, 1 for male. How much time the customer spent i..
find the center and the radius of the circle with equation (4x^2+40x)+(4y^2-8y)=-20
From a group of 8 women and 6 men, a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible?
The base of an aquarium with volume V = 220 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
Sheila has 25/72 ounces of gold. Bill has 7/30 ounces of gold. How much must Kelly have so that they have a combined 1 full ounce of gold?
A rancher has 300 feet of fence to enclose 2 adjacent pastures.
Using the Die class defined in this chapter, write a class called PariOfDice, composed of two Die objects. Include methods to set and get the individual die values, a method to roll the dice, and a method that returns the current sumof the two die..
1. construct an explicit deformation retraction of the torus with one point deleted onto a graph consisting of two
Coffee is being poured into a mug at a constant rate. Sketch a rough graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity. What is the significance of the inflection point?
A 1024 × 768 image is displayed, noninterlaced, at a rate of thirty frames per second.
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