January 2021

A data center contains 1000 computer servers. Each server has probability 0.003 of failing on a given day. a. What is the probability that exactly two servers fail? b. What is the probability that fewer than 998 servers function? c. What is the mean number of servers that fail? d. What is the standard deviation […]

1.   Let X ∼ Poisson(4). a.  Find P(X = 1) b.   P(X = 0) c.   P(X <> d.   P(X > 1) e.   µx f.      µx 2.   The number of pits in a corroded steel coupon follows a Poisson distribution with a mean of 6 pits per cm2 . Let X represent the number of pits

One design for a system requires the installation of two identical components. The system will work if at least one of the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9,

In 1 to 2 pages (approximately 250 to 500 words) double-spaced, 12-inch font, 1 inch margins, please write an essay that answers the following questions. Make an argument, state it clearly in your thesis statements, and use our readings and lessons to evaluate and analyze the argument. The essay must incorporate at least 3 different

1.   The resistance R (in ohms) of a cylindrical conductor is given by R = kl/d 2 , where l is the length, d is the diameter, and k is a constant of proportionality. Assume that l = 14.0 ± 0.1 cm and d = 4.4 ± 0.1 cm. a.  Estimate R, and find the

1.  Refer to Exercise 12 in Section 3.2. Assume that τ0 = 50 ± 1 MPa, w = 1.2 ± 0.1 mm, and k = 0.29 ± 0.05 mm−1 . a.  Estimate τ, and find the uncertainty in the estimate. b.  Which would provide the greatest reduction in the uncertainty in τ: reducing the uncertainty

1.  The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3 , L = 1.2 ± 0.1 cm, and A =

The lens equation says that if an object is placed at a distance p from a lens, and an image is formed at a distance q from the lens, then the focal length f satisfies the equation 1/f = 1/p + 1/q. Assume that p = 2.3 ± 0.2 cm and q = 3.1 ±

1.  Refer to Exercise 12. a.   Let Z = X + Y represent the total number of repairs needed. b.  Find µZ . c.    Find σZ . d.   Find P(Z = 2). 2.   Refer to Exercise 12. Assume that the cost of an engine repair is $50, and the cost of a transmission repair is

Refer to Exercise 4. Assume that the cost of repairing an assembly whose clearance is too little is $2, and the cost of repairing an assembly whose clearance is too much is $3. a. Express the total cost of repairs in terms of X and Y. b. Find the mean of the total cost of