*** SOLVE 8 *** -7. Let X,, X,.. be a sequence of i.i.d. r.v.'s from NCO,...
3.13 Let X,..., X be i.i.d. r.v.'s from the Gamma distribution with parameters a known and β θ eQ (0,0) unknown. (i) Determine the Fisher information I(e). U = U (X, , ,X" ) = ' (ii) Show that the estimate ηα 1.1 is unbiased and calculate its variance.
Let X1,..., X, be an i.i.d. sample from a Rayleigh distribution with parameter e > 0: f(x\C) = e ==/(20?), x20 (This is an alternative parametrization of that of Example A in Section 3.6.2.) a. Find the method of moments estimate of e. b. Find the mle of C. Find the asymptotic variance of the mle.
Please let me know how to solve 7.6.5.
6.5. Let Xi, X2,. .. X, be a random sample from a Poisson distribution with parameter θ > 0. (a) Find the MVUE of P(X < 1)-(1 +0)c". Hint: Let u(x)-1, where Y = Σ1Xi. 1, zero elsewhere, and find Elu(Xi)|Y = y, xỉ (b) Express the MVUE as a function of the mle of θ. (c) Determine the asymptotic distribution of the mle of θ (d) Obtain the mle of P(X...
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ANSWER NUMBER 8, NOT NUMBER 7
THIS IS THE THIRD TIME IM UPLOADING THE SAME QUESTION, PLEASE
READ THE WRITTEN DESCRIPTIONS
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Let X1, X2, ..., Xn be i.i.d. r.v. Let X1,Xy, , Xn be i.id. r.v.'s with pdf f(x,8) = e-(x-91(9M)(x), where θ E R. a) Find the distribution of Y X(1). b) Construct a pivotal quantity based on Y. c) Use part b) to construct a 1-α confidence interval for θ. d) What is the shortest confidence...
5.7 Let X, X, be independent r.v.'s from the u(e -a, o+ b) distribution, where a and b are (known) positive constants and θ Ω M. Determine the moment estimate θ of θ, and compute its expectation and variance.
As on the previous page, let Xi,...,Xn be i.i.d. with pdf where >0 2 points possible (graded, results hidden) Assume we do not actually get to observe X, . . . , Xn. to estimate based on this new data. Instead let Yİ , . . . , Y, be our observations where Yi-l (X·S 0.5) . our goals What distribution does Yi follow? First, choose the type of the distribution: Bernoulli Poisson Norma Exponential Second, enter the parameter of...
P(8), θ eQa(0 4.6 Let X, ..., X, be independent r.v.'s distributed as estimate δ(x , , x )-r and the loss function L ( , δ)-[8-6(5- ,o0 ), and consider the -5)]218. E,[e-5(X, ,X,)],andshow that it isin dependent ofe. R(0:δ)- (i) Calculate the risk (ii) Can you conclude that the estimate is minimax by using Theorem 9?
Question 8 using the
information from question 7 for b-d
s (z .d. r.v's with pdff(x;8)-e-(x-θ)|(9 )(x), where θ E R LetX1,Xy, a) Find the distribution of Y -X(1) b) Construct a pivotal quantity based on Y. c) Use part b) to construct a 1-α confidence interval for θ d) What is the shortest confidence interval of the form obtained in part c)? Xn be i.i 8.) Let X1, X2,., Xn be a random sample with pof 2θ a) Find...
3.4 Let X,, X be a random sample of size n from the U(Q,62) distribution, 6, and let Y, and Yn be the smallest and the largest order statistics of the Xs (i) Use formulas (28) and (29) in Chapter 6 to obtain the p.d.f.'s of Y and Y and then, by calculating depending only on Yi and 1,- Part i. (Note: it is not saying to find the joint pdf of Yi and Yn Find their marginal Theorem 13...
Can you help me to solve this problem
P5.30 Let X (k) be the 8-point DFT of a 3-point sequence x(n)- 15, -4,3). Let Y(k) be the 8-point DFT of a sequence y(n). Determine y(n) when Y (k) -Ws*X(-k)s.
P5.30 Let X (k) be the 8-point DFT of a 3-point sequence x(n)- 15, -4,3). Let Y(k) be the 8-point DFT of a sequence y(n). Determine y(n) when Y (k) -Ws*X(-k)s.