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- 12) A metal bar is heated, and then allowed to cool. Its temperature T (in °C) is found to be The time is in minutes. T=15+75e-0.25 t Find the time rate of change of temperature after 5.0 minutes. 13) The standard normal curve (sometimes called the bell curve) in statistics looks like: 1 -x² y = e 2 √2π Show that there are two inflection points at x = +15.3-2 The random variable X has probability density function - {2(1-x). 0, 5.3-3 f(x) = 0 b probability histogram of the data. 2(1-x). 0≤x≤ 1, otherwise. Graph the probability density function of X. Find and graph the cumulative distribution function of X. Generate 1000 values for X and make an empirical probability histogram of the data. The random9. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.
- There are two Gaussian curves below (Plots A and B), along with the respective R source codes.Looking at the plots and the source codes provided, identify the parameters of respective Gaussian pdf's (probability density functions) and the numeric value of x in the PDF F(x)express the areas under the curves in terms of F(x). ( Do not calculate those areas.Your answers must be like F(x) or 1- F(x) for a relevant value of x.) Below is the source code and image for part B13 Let X be the standard normal distribution and consider the transformation given by Y = 1/X. Select all answers that apply. Select all answers that apply. Note exp(z) = e^z %D %3D Choose all that apply. O The density of Y is: g(y) = (1/2*pi)^(1/2) * (1/y^2)*exp(-1/(2y^2)) The density of Y is: g(y) = (1/2*pi)^(1/2) *exp(-1/(2y^2)) The values of y for which the density is non zero is y0. The values of y for which the density is non zero is y>0. %3D12
- The life of an automotive component can be modeled by Weibull distributionα =6.2?105 and β =1.3.(i) Calculate the cumulative density function, F (t) Deming believes poor quality was not the fault of workers but as a result of poor management of systems for quality improvement.(ii) Do you agree with the statement? Why do you agree or disagree? (iii) Calculate the reliability function, R (t), and the hazard function, h (t) at the end of the rotating period of 36000 miles.Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.Question 37 and 38.