9. A Gaussian distribution is given by p(x) = Ce-Ax-a)*. Calculate the following integrals. In these problems you can look up integral tables located on the back cover of our class textbook or elsewhere, or use a webserver such as Wolfram alpha. a) l, = S e-2(x-a)³dx b) l = xe-A(x-a)*dx c)Iz = [x²e¬a(x-a}*dx -8- -08-

1. Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second when pressure drops sufficiently to allow the water to dissociate into water vapor, forming a gas bubble behind the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to occur. Eight tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed x = 102.2 meters per second. Assume that speed is normally distributed with known standard deviation o =4 meters per second. 1.1. Test the hypothesis H0 : µ=100 versus H1: µ < 100 using a=0.05. 1.2. What is the P-value for the test in part 1.1.? 1.3. Compute the type II error if the true mean speed is as low as 95 meters per second. 1.4. What sample size would be required to detect a true mean speed as low as 95 meters per second if you are willing to accept a type Il error of 0.15?

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5. Find the average value of f(x) == on [e¹, e5]. X

/www.mathxl.com/Student/PlayerHomework.aspx?homeworkld=611416809&questionld=1&flushed%3false&cld%3D6709552¢erwin-yes MAT 234-KA: Elementary Differential Equations junior E Homework: Section 7.4 HW Score Question 4, 7.4.26 > points O Points Determine L{F}. 8s - 14s- Ss+7 F(s) = s (s - 7) %D Clear all View an example Get more help - Help me solve this