A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, $ r = P(\#2 \text{ fails} \mid \#1 \text{ fails}) > P(\#2 \text{ fails}) = q $. If at least one pump fails by the end of the pump design life in 12% of all systems and both pumps fail during that period in only 8%, what is the probability that pump #1 will fail during the pump design life?[Answer box here for user input]

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Answered: A system consists of two identical…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You are a statistician working at a small, but premium gourmet bakery. Your bakery can produce up to 4 elaborate custom wedding cakes per week (constrained by design time, bake time, and craft time). If weekly demand is greater than the four cakes you can make, you lose sales as the customers will order from the inferior-but-faster Amazon Baking Company instead (so, there are weeks that the demand for your cakes is not met). Each wedding cake costs 300 dollars (labor + materials) to produce, but sells for $1000. You estimate that the probability distribution of weekly demand for custom wedding cakes is as follows: Demand 0 1 2 3 4 5 6 7 Probability 0.05 0.05 0.10 0.20 0.40 0.10 0.05 0.05 What is the expected profit each week from wedding cake sales? (Hint: Remember, some sales will go elsewhere if you are at maximum crafting capacity.)
A researcher wants to study the factors affecting a person's decision to buy a car. For his study, he selects a random sample of 100 people from a city and estimates the following regression equation: C = - 7.35 + 0.44/+ 0.36M – 0.27P, where C is a binary dependent variable which denotes the decision to buy the car (C equals 1 if the person decides to buy the car, and 0 otherwise), / denotes the monthly income of the person (I equals 1 if the income exceeds $5,000 and 0 otherwise), M denotes the car's mileage (measured in miles per gallon) and P denotes the price of the car (in thousand dollars). The researcher wants to test the hypothesis that the coefficient on /, B4, and the coefficient on M, B2, are jointly zero, against the hypothesis that at least one of these coefficients is non-zero. The test statistics for testing the null hypotheses B1 =0 and B = 0 are calculated to be 1.55 and 1.25, respectively. Suppose that these test statistics are uncorrelated. The F-statistic associated…
A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.
1.2.4. Consider the spreading of a highly communicable disease on an isolated island with population size N. A portion of the population travels abroad and returns to the island infected with the disease. Formulate a dynamical system to approximate the change in the number of people in the population who have the disease.
#14).
Consider the model Y = ß0 + B₁X1 + ß₂X2 + B3X³ + B4X4 + €. If it is suggested to you that the two variables Z₁ = X₁ + X3 and Z2 = X₂ + X4 might be adequate to represent the data, what hypothesis, in the form C3 = 0, would you need to test? (Give the form of C.)
This is System Modeling & Simulation question
Table 3-4 Assume that Andrea and Paul can switch between producing wheat and producing beef at a constant rate. Minutes Needed to Make 1 Bushel of Wheat Pound of Beef 15 Andrea 30 Paul 15 5 efer to Table 3-4. Which of the following combinations of wheat and beef could Andrea produce in one 8-hour day? O a. 16 bushels of wheat and 32 pounds of beef O b. 9 bushels of wheat and 25 pounds of beef O c. 7 bushels of wheat and 15 pounds of beef O d. 10 bushels of wheat and 13 pounds of beef
An industrial concern has experimented with several different mixtures of the fourcomponents—magnesium, sodium nitrate, strontium nitrate, and a binder—that comprise arocket propellant. The company has found that two mixtures, in particular, give higher flare illumination values than the others. Mixture 1 consists of a blend composed of the proportions.40, .10, .42, and .08, respectively, for the four components of the mixture; mixture 2 consists ofa blend using the proportions .60, .25, .10, and .05. Twenty different blends (10 of each mixture)are prepared and tested to obtain the flare-illumination values. These data appear here (in unitsof 1,000 candles).Mixture 1 185 192 201 215 170 190 175 172 198 202Mixture 2 221 210 215 202 204 196 225 230 214 217a. Plot the sample data. Which test(s) could be used to compare the meanillumination values for the two mixtures?b. Give the level of significance of the test and interpret your findings
Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?b) Suppose x2 increased by 2 units. What would be the expected change in x1?c) Suppose x2 decreased by 4 units. What would be the expected change in x1?
3. Find the the equation of the least squares regression line for the data as the linear model f(x) = ao + a₁x in the manner discussed in the textbook using the formula A = (XTX)-¹XTY. What are your values for ao and a₁?
#14).

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