Concept explainers
The joint distribution for the length of life of two different types of components operating in a system was given in Exercise 5.18 by
The relative efficiency of the two types of components is measured by U = Y2/Y1. Find the
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Chapter 6 Solutions
Mathematical Statistics with Applications
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardIdentify the estimates and estimators from the model (p1). What is thedifference between estimates and estimators?arrow_forward
- Q1: The data points below are related to a chemi-thermo-mechanical pulp from mixed density hardwoods. They relate Y (specific surface area of the fibres in cm/g) to the % NaOH (sodium hydroxide) used as a pretreatment chemical and the treatment time (min) for different batches of pulp. The variables are present at three different levels. In this case, it is preferred (for reasons that we will discuss later in the course) to code the levels as shown in the last two columns of the table below, designated by Xı and X2. Y SODIUM ΤΙME Xi X2 HYDROXIDE 5.95 3 30 -1 5.60 3 60 -1 5.44 3 90 -1 1 6.22 9. 30 -1 5.85 9 60 5.61 9. 90 1 8.36 15 30 1 -1 7.30 15 60 1 6.43 15 90 1 1 a. Using the variables Y, X1 and X2 (not actual time and sodium hydroxide! You will see why later!), fit the following multiple linear regression model to the data: (Model A) Y = (b0) + (b1) X1 + (b2) X2; subsequently, estimate the parameters and examine the residual plot (residuals vs Y hat). What does this residual plot…arrow_forwardSuppose an animal scientist, Dr. Dew believes that birth weight (in kg) explains the variation in the length of gestation (in days until birth) for various mammals. To support this fact, he collected data and found out that when the birth weight was x = length of gestation was y = Hint: E,(x; – 7)² = 540, 916.8, E, (y: – 9)² = 195, 233, and E:(yi – ŷ)² = 181, 018. {60, 110, 44, 900, 107} the 241.61+0.162x. {122, 241, 61, 365, 617}. The fitted model was ŷ a) Ignore the birth weight (x). If the length of gestation are independently and identically distributed (i.i.d.) with mean u and variance o?, what is the estimate for u and o?, respectively? b) If you now use the birth weight (x) and assume that the length of gestation are (i.i.d.) with variance o? and mean µ Bo + B1X. (i) Compute the estimate for o?. (ii) By comparison to your estimate in part (a), what does this tell you about this model? c) Construct a 95% confidence interval for the slope parameter.arrow_forward7 & 15.arrow_forward
- 1. In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)? 2. The relationship between weight and age was found to have a linear relationship, with expression weight= 3.0 (age) +10. Predict the weight of a girl whose age is 20 years? 3. A. If a z score of 1.95 is equal to a p of 0.9744, what proportion is greater than1.95 B. From question A, what proportion is between the mean and 1.95? 4. If a the constant for a regression is 0.8 and the standard deviation for the x variables is 4 while the standard deviation for the y variables is 6. What is the correlation coefficient r? 5. In a class of 20 students, twelve take mathematics and genetics, while eight take genetics only. What is the probability of selecting a student who takes only mathematics?arrow_forwardEngineers at a large company are trying to investigate if there is any difference in the average wear of brand A, brand B or brand C tires for the company's new models. To help them arrive at a decision, an experiment is conducted using 11 of each brand. The tires are run until they wear out. The results ( in kilometres) are as follows: Brand A: xī = 37,900 S1 = 5100 Brand B: X2 = 39,800 S2 = 5900 Brand C: X3 =38,500 S3 = 5600arrow_forwardPlease help me answer (d) and (e).arrow_forward
- A scientist has measured quantities y, x1,and x,. She believes that y is related to x, and x2 through the equation y = ae+Px2 8, where & is a random error that is always positive. Find a transformation of the data that will enable her to use a linear model to estimate B, and B,.arrow_forwardSuppose a logistic regression model is fitted for the probability of car ownership for residents of a certain city in Oman (Y=1 if a resident owns a car, Y=0 if a resident does not own a car). Suppose the explanatory variables used are x1=no. of years a resident spent in schooling and x2 is gender of the resident of the city (x2=1 for a male and x2=0 for a female resident) a) Interpret el and e82 b) if BO= -1.6, B1=0.4 and B2=3, estimate the probability of a resident in the city owning a car.arrow_forwardThe following data shows the atmospheric pollutants yi(relative to an EPA standard) at half hour interval xi. Find the equation y=a+bx of the least square line that best fits the data points given by 2,1, 5,2, 7,3, 8,3. Hence predict the atmospheric pollutant at x=6 half hour.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning