1.Social distancing is an important measure to prevent the spread of COVID-19. Assume that the chance, denoted by r, that a healthy person gets infected by a viruscarrier who is L metres away is modelled by r = exp{-L²/7²}, where y> 0.(a)Discuss mathematically how r changes as L and y change in the specifiedmodel.Give your practical interpretation of y and list at least FOUR real-world(b)factors that you think may affect the magnitude of y.(c)Assume that a virus carrier is at location c on a road with infinite length,and a healthy person is on the same road at location X, which is normally dis-tributed with mean u and standard deviation o. Calculate the expected chance thatthe healthy person will get infected.Following the Government's two metre social distancing guidance, we(d)assume that the distance between the location of the virus carrier and the expectedlocation of the healthy person is 2 metres. Find the value of y such that the maxi-mum expected chance that the healthy person gets infected is 10%.(e)Discuss and justify at least two limitations of the specified model for r.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. y 0.3 0.2 Mean Temperature (x) 0.1 0.0 -0.1 6.22 8.01 5 8.67 10.61 12.5 11.94 12.55 18.03 18.24 (a) Construct a scatterplot of the data. 19.94 20.3 19.02 17.78 19.67 USE SALT Net…
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The line of best fit through a set of data isy=46.539+4.023xy=46.539+4.023xAccording to this equation, what is the predicted value of the dependent variable when the independent variable has value 40?y = Round to 1 decimal place.
15) The intercept is 0, the autoregressive coefficient is 0.2 and the moving average coefficient is 0.5 in an ARIMA(1,1,1) model. What is the one-step ahead forecast if the shock for the current period is -2 and the current and one-period lagged values of the forecast variable are 110 and 105?
11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2. a) Complete the ANOVA table. b) Find the t-stat of the co-efficient of X c) Find the co-efficient of X.
A study reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment. With age = x and ACBG = y, summary values are n = 26, Ex; = 1613, Σ(x; − x)² = 3756.96, Ey, = 281.9, Σ(y₁ - y)² = 465.34, and Ex,y; = 16,711. (a) Compute a 90% CI for the true correlation coefficient p. (Round your answers to four decimal places.) (b) Test Ho: P = -0.5 versus H₂: p < -0.5 at level 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. There is no evidence that p < -0.5. O Fail to reject Ho. There is evidence that p < -0.5. O Fail to reject Ho. There is no evidence that p < -0.5. O Reject Ho. There is evidence that p < -0.5. (c) In a regression analysis of y on x, what proportion of variation in change of cortisol-binding globulin level could be explained by…
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We are interested in estimating the following model log(wage) = Bo + Bieduc + Bzexper + u where • wage=hourly wage, in US dollars; • educ=number of years of education; • exper=number of years of work experience. The variable ctuit is the change in college tuition facing students from age 17 to age 18 and is used as an IV for educ. We run the first stage regression for educ and get the following output: Source s df MS Number of obs 1,230 F (2, 1227) 550.19 Model 3220.84426 2 1610.42213 Prob > F 0.0000 Residual 3591.43541 1,227 2.92700523 0.4728 R-squared Adj R-squared 0.4719 Total 6812.27967 1,229 5.54294522 Root MSE 1.7108 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] ctuit -.1859575 .0608175 -3.06 0.002 -.3052752 -.0666398 exper -.521161 .0157156 -33.16 0.000 -.5519933 -.4903286 _cons 18.63905 .1757961 106.03 0.000 18.29415 18.98394 Is the assumption of instrument relevance satisfied? Why yes, or why not?
Please solve 12.7 and dont use any programme like minitab.

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