The density function of the time to failure in years of the gizmos (for use on200widgets) manufactured by a certain company is given by f(t)t 2 0.3(t +10)³(a) Derive the reliability function and determine the reliability for the firstyear of operation.(b) Compute the MTTF.

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Answered: The density function of the time to…

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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A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.
The heat index (HI) is an estimate of the temperature felt by the human body based on the actual measured air temperature T (in °F) and relative humidity h,. It is given by HI = - 42.379 + 2.049015237 + 10.14333127h, – 0.22475541Th, – (6.83783 × 10-³)T² - (5.481717 x 10-3)h,² + (1.22874 × 10-³)7°h, + (8.5282 - 10-4)Th,² - (1.99 x 10-")T®h,?. a. If the air temperature in your area is 107°F with a relative humidity of 8%, how hot does your body feel? b. If the air temperature and relative humidity is known to be increasing at a rate of 2°F per sec and 1% per sec, resp., how fast is the heat index changing at the moment when the air temperature in your area is 107°F with a relative humidity of 8%?
A quality control team studies the relationshipbetween years of experience (x) for individualdesign employees and ability to complete acomplex project within a certain time frame (y),where Y = 1 if the project is successfullycompleted, and Y = 0 if not. We know: b0 = −1.68and b1 = 0.12.a) Write the estimated logit function.b) Estimate the odds that a design employeewith 10 years of experience completes thecomplex project.c) Find and interpret the estimated odds ratiofor this model.
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): X 1= average high school grade in mathematics (HSM) X 2 = average high school grade in science (HSS) X 3 = average high school grade in English (HSE) X 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: SOURCE DF MS F VALUE PROB>F MODEL 28.64 5.73 11.69 0001 ERROR 218 106 82 0.49 TOTAL 223 135.46 ROOT MSE DEP MEAN 0.700 R-SQUARE 0.211 4.635 ADJ R-SQ 0.193 PARAMETER STANDARD T FOR O VARIABLE ESTIMATE ERROR PARAMETER -0 PROB> ITI INTERCEPT 2.327 0.039 5.817 0.0001 0.0003 XI HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV) 0.146 0.037 3.718 a.036 0.038 0.950 0.3432…
7 In a G/G/3 system with average service time equal to 6.9 minutes, average time in system equal to 25.1 minutes, what is the average wait in queue?
Please solve 12.7 and dont use any programme like minitab.
Consider the logit regression log(odds(QualExam) = ßo + B, • ParEduc + B, • Awards. where QualExam is a binary variable that indicates passing the exam if equal to 1, and failing the exam if 0, ParEduc indicates the parents' education level, and Awards is a binary variable that indicates having experience of obtaining award(s) if equal to 1, and not having experience if 0. Given the parents' average education level unchanged, the odds ratio is expected to be _ for an individual with awards to pass the exam comparing to those without awards. For an individual without awards and the parents' education level of 4, the estimated probability of passing the exam is approximately_. ParEduc Awards Intercept -10.53 2.98 0.48 O A. 0.48; 80%. O B. 1.616; 80%. O C. 1.616; 4%. O D. 0.48; 4%.
You are an econometrician working in the Ministry of Finance in Trinidad and Tobago and using a database consisting of 108 monthly observations on automobile accidents for Trinidad and Tobago between January 2011 and December 2019, you estimate the following model: log( totacc,) = B, + Bit + B2feb, + ßzmar.. + B12dec, + µe where totacc is the total number of accidents, t is time (measured in months), and feb,, mar,, dec, are dummy variables indicating whether time period t corresponds to the appropriate month. You obtain the following OLS results: Number of obs F( 12, Prob > F df 108 31.06 0.0000 0.7969 Source I MS 95) Model | 1.00244071 Residual | .255496765 12 .083536726 95 .00268944 R-squared Adj R-squared = 0.7712 Root MSE Total | 1.25793748 107 .011756425 - .05186 ltotacc | Coef. Std. Err. t P>It| [958 Conf. Interval] .0024274 -.0912208 .031287 .0027471 .0001611 .0244475 .0244491 17.06 0.000 .0030669 .0058479 .1283621 feb | -.0426865 mar | apr | may | jun | jul | aug | sep I oct I…
When we fit a logistic regression model with a single explanatory term, x, we often assume that logit (pi) Bo + ₁x₂ where, for the ith observation, p; is the probability of a trial being successful and *; is the value of the explanatory variable. Which of the following is a good reason for using the logit link function? We can't use more than one explanatory term unless we use this link function. It allows us to model nonconstant variance in the response variable. It ensures that the probability of success is between 0 and 1. It ensures that the variance of the response is the same for all observations.
Pison/&user=tmorrison7&key%3DrotNBBCzVIsGRqZV8t.. Previous Problem Problem List Next Problem (1 point) Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Subject 1 3 4 7 8 9 10 11 12 13 14 15 16 Empathy Score 41 48 39 56 64 63 59 53 Brain Activity -0.127 0.3910.02 0.378 0.015 0.404 0.11 0.513 0.149 0.736 0.254 0.573 0.217 0.72 0.355 0.786 47 52 64 73 12 68 28 120 1.2 sub ject Z F20 10,0 120 -8.4 Given that the equation for the regression line is y = 0.00619x +0.00032, what is…
Consider the logit regression log(odds(QualExam)) = B, + B, * ParEduc + B2 + Awards, where QualExam is a binary variable that indicates passing the exam if equal to 1, and failing the exam if 0, ParEduc indicates the parents' education level, and Awards is a binary variable that indicates having experience of obtaining award(s) if equal to 1, and not having experience if 0. Given the parents' average education level unchanged, the odds ratio is expected to be for an individual with awards to pass the exam comparing to those without awards. For an individual without awards and the parents' education level of 4, the estimated probability of passing the exam is approximately_. Intercept ParEduc Awards -10.53 2.98 0.48 O A. 1.616; 4%. O B. 1.616; 80%. O C. 0.48; 4%. O D. 0.48; 80%.

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The density function of the time to failure in years of the gizmos (for use on 200 widgets) manufactured by a certain company is given by f(t) %3D (t +10) (a) Derive the reliability function and determine the reliability for the first year of operation. (b) Compute the MTTF.