Example 15: (i) Find the M.L.E. of the parameter a of the population having the density function f(x, y) = 2 (a - x), 0
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- The length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 5X-4, where X has the following density function. Find the mean and variance of the random variable Y. 1 f(x)=2' X 2 x>0 0, x≤03. 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)For x, y ≤ (0, ∞), let X and Y have the joint density 1 -e Y f(x, y) = Y i) Compute the marginal density of Y. ii) Compute the conditional mean and variance of X given Y = y. iii) Compute Var(X).
- There are two components in an electronic system. Let X and Y denote the lengths of life in years. The joint density function of these variables f(x, y) = {ye-&+x) ,x 2 0, y Determine P(x>3) What is the probability that both components will exceed 3 years?2. An investor's losses follow a distribution with density function, f(x) =, x > 1 and 0 everywhere else, To recover her losses, the investor purchases an insurance policy with a deductible of $1. Show that the insurance company will go bankrupt. Hint: The expected amount of the losses paid by the company is too large.Suppose that an automobile dealer pays an amount X (in thousands) for a used car and then sells it for an amount Y. Suppose that X and Y have the joint density fxy (x, y) = for 0 < x < y < 6. The dealer's expected profit (in thousands) from the sale is equal to
- "Medians, etc problem." Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.1) Consider a continuous RV, Y, with a pdf given by f(y)=ce²¹, -∞A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is fo fkr², if 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman