3. A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(x; 8) = )xe, x>0 хе elsewhere That is, Y has a gamma distribution with parameters a = 2 and 0. Let ô denote the MLE of 0. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a. Find the MLE of 0. b. Find E(Ô) and V (ô) c. Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation.
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- QI. The probability mass function of a random variable X is given by p(i) = ca' /i!, i = 0,1,2,..., where à is some positive value. Find (a) P{X = 0} and (b) P{X > 2}. %3D9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(y|0)= { (1) y> 0, otherwise. That is, y has a gamma distribution with parameters α = 2 and 0. Let Ô denote the MLE of 8. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of 0. b Find E() and V (8). c 82 ye-3/0 Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?5.4.6 WP Determine the covariance and correlation for the joint probability density function fry(x, y) = e* over the range 0< x and 0 < y.
- 1.4 The pH of milk samples from Dairy Belle is a random variable Y with probability density function given by ((1/9)(4 – y)?,5Consider the following probability density function, what is the F(14) 0.22 x = 7 x = 9 x = 11 x = 13 x = 15 x = 17 0.22 0.05 0.05 f(x) = %3D 0.06 0.33 0.06 0.01 x= 19 x = 236.106 If Y is a continuous random variable with distribution function F(y), find the probability density function of U = F(Y).1. Develop a random variate (composition method) generator for the random variable X with the probability density function where I represents the indicator function. 5 f(x)=e*I(x 0) 4 a. Implement this generator to generate 500 random variates. b. Compute the sample mean and sample variance of these 500 variates and compare with the theoretical values. c. Plot the histogram of these 500 variates and compare the histogram with the graph of f(x).1. The density function for random variable X is f(x). Find variance for the random variable X. Leave your answers as reduced fractions. f(x) = {16 x+05. Determine the value of c that makes the function f (x, y) = c(x + y) a joint probability density function over the range 0 < x < 3 and 0 < y < x. Answer is C = 2/27 a. From the answer in Question 5, Determine the marginal probability distribution of X. b. From the answer in Question 5, Determine the conditional probability distribution of X given that Y = 2. c. From the answer in Question 5, Determine E(Y | X = 1). (up to 6 decimal place)Question 37 and 38.2.4 Solve the below problem: The change in depth of a river from one day to the next, measured (in feet) at a specific location, is a random variable Y with the following density function: - 3 < y< 3, f(y) = (0, elsewhere. 2.4.1. What type of distribution does Y follow? 2.4.2. Find E (Y) (Hint: Use the distribution function).Given the function y = x2 considered as a probability density distribution defined at 0 ⩽ x ⩽ 3. Between which percentiles will the central 30% of the observations be found from the Integral Function?Recommended 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