Use the method of moment to estimate the parameter 0 for the density f (x; 0) =; I[0,0](x) based on a random sample X1,X2,...,Xn. Give a sufficient statistic for 0.
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based on a random sample X1, X2,...,Xn. Give a sufficient statistic for 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bf7f571-1f5c-4f23-a40a-002fd0e5042d%2F52d75757-5461-4413-a491-021a6551bc42%2Fs0swa0g_processed.png&w=3840&q=75)
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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.025. (8 pts) X is a random variable with pdf Xe-xx>0 f(x) = { o/w and let Y = 1-X/2. Find the pdf of Y with the support of g(y).Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?
- Let Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s2 is known. Find the Score function, the estimating equation and the information matrix.Normal distribution. The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.Be X a random variable with density function defined by f(x) = -2², , x>0. 3 Get the moment-generating function and based on it, calculate the average and variance of X.
- Let X be the random variable having pdf f(x) = 1,0 < x < 1, zero e.w. Compute the probability of the range of the random sample of size 4 (X1, ., X4) is less than 1/2. Hint: Range is R = X(4) – X(1).* The waiting time T (in hours) between each SMS you receive is random with the density function. f(t)=1,8e1,8t , t> 0 1- Find the expected time between SMS and find the corresponding variance.Exercise 15. Let X be a continuous random variable with PDF given below. fx(z) = ;(x+1)/-1,1(z) Use the generalization of method 2 to find the distribution of Y = X².
- Suppose that X1,..., X, is a random sample from a distribution with density f(x; 8) = 0x=2, x € (0, 00) and parameter 0 > 0. What can you say about the method-of-moment estimator of 0 as we defined it in the lectures?Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of YQ4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.
