12 Let X be a random variable with mgf(t) = 0.6e' + 0.3e2t + 0.1e3t Find E(X) For the instructor, this was question 17.
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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 = +1Use the following data to answer question 8 - 12. A number of studies have claimed evidence that the first-born in a family is, on the whole, more likely to be "successful" than later-borns. A study along this direction compared the IQs of a random sample of 80 first-borns with those of an independent random sample of 105 later-borns. The data are summarized below: Sample size Sample mean Sample SD First-borns 80 112 7.2 Later-borns 105 108 8.0Y has a distribution function (0, ys0, 24 F(y) = 0A researcher administers a treatment to a sample of n=36 selected from a population with u=30 and o=2. If the sample mean after treatment is M=32, then Cohen’s d=1.00. True or False?9. 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.In how many ways can a row of three contestants for a TV game show be selected from an audience of 364 people? ways10. A sample of high-capacity resistors is tested until failure and the results fitted to a Weibull probability model. Based on these tests, the reliability function of a resis- tor is estimated to be -0.0013 rl.83 R(1) = e' a. What is the failure rate function for these resistors? b. Is this resistor more likely to fail as it ages? c. What is the probability that a resistor will function for more than 30 hours with- out failure? d. Suppose that a resistor has been operating for 50 hours. What is the probability that it fails in the 5 1st hour? [Use the results of part (a) for your calculations.]Please help me with the following question14. Show that for the Gamma distribution e dp = dx, 0Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON