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- 5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?2. Let X₁,..., Xn be iid observations from a pdf defined by 0 f(x|0) = 0 0. (1+x)¹+0¹ Find a complete sufficient statistic.Q.2 Let X has the following probability density function: fx(x) = a e-ax;x > 0 Find moment generating function and then using it find mean and variance. End of Quiz
- Use R to complete the following. R code and R output are requested for solution. Please keep your solution clear and easy to read. Unclear solution will not be grade. O for manual solution. Carry out a simulation experiment to illustrate the central limit theorem when the population distribution is arcsine with probability density function f(x) = 1 T√x(1-x) x = (0, 1). Consider the four sample sizes n = 1, n = 3, n = 5, n = 10, and in each case use 10,000 replications. Note: To simulate a random sample of size n from the arcsine distribution in R, use the command rbeta(n,1/2,1/2).الموافق foo an exponentiaL distribution fx Cx jt) e.w. where u>o Write (Dankderive) meancespedoed V9lue) f.eECx)9.12 question attached4.32 Weekly CPU time used by an accounting firm has probability density function (measured in hours) given by | (3/64)y²(4 – y), 0EL 466 416 13.) The continuous random variable (RV) X is uniform over [0,1). Given Y = -ln X what is P({0Q.1Let X be a random variable normally distributed with mean μx 1. Find the mean μy of Y. 2. Find the standard deviation oy of Y. 3. Find the PDF fy of Y and evaluate fy (5). (My, oy, fy (5)) = ___________). = 6 and standard deviation ox = 4. Let Y = 4X + 5.Ук. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of BNeed sol of b part only. Within 20 minutes.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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