1. Handin Suppose that Y,, Y2, ...,Yn constitute a random sample of size n from the density function fyl®) = {(@ – 1)eº(-tny), 0, 01 elsewhere. 4.1. Obtain the MLE for 0.
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- Please be specific.3. Suppose Y is a random sample of size 1 from a population with density function Oyº-1 0 0.5. (b) The hypotheses are Ho : 0 = 0, versus Ha : 0 > 00. What is the value of 00 if the signficance level of the test specified in (a) is 0.10? (c) Suppose a random sample of n = 7 observations is taken from this population to test the hypotheses Ho : 0 = 2 versus Ha : 0 > 2. As a decision rule, the experimenter plans to record X, the number of that exceed 0.9, and reject if X > 4. That is, the experimenter plans to use the test: ys 1 X >4 $(X) = { 0 x < 4 What is the probability of making a Type I error? Need Your Help with Part - (c)8. Let (11, 12, f(x) = e-(=-a), x > a. Find an estimator, â, of a by method of moments. .., Tn) be independent measurements of a random variable X with density function
- Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by 3y2 0 < y< 0, f (y|0) = өз 0, elsewhere. 1.1. Show that Y(n) max(Y1, Y2, ... , Yn) is sufficient for 0.9. A cylindrical soft drink can has radius of the base Y and height Y2 (in cm³). Suppose that Y, and Y, are jointly continuous random variables with the following joint density function: . 9 (80y1y2-20yy2 - 4y1+ yiy) 0 S yn < 4, 0 < Y2 < 20 f(yı, Y2) = 0. 128000 elsewhere Find average volume of can.The probability density function of a random variable Y is given by 24y(10+2y- 0.3y²) S; (y)=< 0 < y<10 10000 0, otherwise Suppose a random sample of 40 observations is obtained from this distribution and these are denoted as Y,,Y,,…,Y40 • 40 a) Approximate the probability that the sample sum T =Ey, is between 200 and 250. i=1 b) Approximate the probability that the sample mean Y is less than 5.5.
- 33.-46. Given that X has a density function 2x 3- x f (x) = for 0tEx. 4. Let X,Y are independent random variables where X ~ N(0, 1) and Y ~ G(1/2, n/2). Let T:= X//Y/n, then show that the density function of T is described as r(n+1)/2) (1+) VnnI'(n/2) -(n+1)/2 fr(t) - (-∞2. Consider the joint density function 16M f(x,y) = {#, z> 2,0: Consider that a random variable Y has the following density function, («y*-1 fG) =} 0a 0sys0 elsewhere where a is known, and satisfies a > 0, and 0 is an unknown parameter. Let Y, be an independent random variable from the distribution f(y), with i=1,..,n a) Calculate the bias for the estimator ê = Ỹ = 2 Y/n. b) Calculate the mean square error of the estimator ô = Y = 2 c) Propose an unbiased estimator of 0 and show that it is unbiased.B1. Let us consider a random variable X following a Weibull distribution with parameter k = 2 and A > 0, which has density function Se-/A)", if x2 0, 0, fx(x) otherwise. Given the following random numbers sampled from the uniform distribution on the interval [0, 1], u1 = 0.1345, u2 = 0.7515, uz = 0.1671, u4 = 0.9101 and uz = 0.0578; compute five sampled values for X for A = 3.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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