1.3. Let Y₁, Y₂, ..., Yn denote a random sample of size n from a population with a uniform distribution= Y(1) = min(Y₁, Y₂, ..., Yn) as an estimator for 0. Show that êon the interval (0, 0). Consideris a biased estimator for 8.

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Answered: 1.3. Let Y₁, Y₂, ..., Yn denote a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a random sample X1,...,Xn,... ∼ iid Beta(θ,1) for n > 2. Prove that the MLE and UMVUE are both consistent estimators for θI got MLE = n/-∑logXi and UMVUE = (n-1)/∑logXi. Need help in proving consistency
Consider a set of data (x;, y;), i = 1,2, .,n and an intercept model given by: 1. Yi = Bo + Ei with E(s;) = 0, Var(ɛ;) = o? and all ɛ,'s are independent and normally distributed. Derive the standard error of the point estimator Bo.
4. Suppose you are given the following information: = 49.6870 – 2.1586X; r2 = 0.9757 (0.7463) (0.12113) df=8 T= (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r2 tell you? c) Perform a hypothesis using r2, such that p=D0, what do you conclude?
4. 65th Pg. 59, 1. 7. 19. * Find the of the distribution having pot F(x) = 1x1/4₂ Percentile where -a, < x < 2, f(x) = 0, elsewhere.
A computer while calculating the correlation co-efficient between the variables X and Y obtained the following values. N = 25 )X= 125 SX2 = 650 2y= 100 EY2 = 460 EXY = 508 It was, however, later on discovered at the time of checking that it had copied down two pairs of observations as : X Y 14 8 While actual values were Y 12 8 Obtained the correct value of correlation coefficient between X and Y.
3.1 Suppose X ~ N(18, 7). What value of x has a z-score of -2.16? Round to 2 decimal places..
3.3.24. Let X1, X2 be two independent random variables having gamma distribu- tions with parameters a₁ = 3, B₁ = 3 and a2 = 5, B2 = 1, respectively. (a) Find the mgf of Y = 2X₁ +6X2. (b) What is the distribution of Y?
4, 12. How Call v. 13. Suppose that two raters (Rater A and Rater B) each assign pirysica attractiveness scO = not at all attractive to 10 = extremely attractive) to a set of seven facial photogranhe 21 %3D Pearson's r can be used as an index of interrater reliability or agreement on quantitative ratings. A correlation of +1 would indicate perfect rank-order agreement between rate while an r of 0 would indicate no agreement about judgments of relative attractiveness An r of .8 to .9 is considered desirable when reliability is assessed. For this example, Rater A's score is the X variable and Rater B's score is the Y variable. The ratings are as followe F follows: Photo Rater A Rater B 1 3. 5. 8. 6. 7. 8. 6. 4. 6. 10 6. 7. 5. 4. a. Compute the Pearson correlation between the Rater A and Rater B attractiveness ratings. What is the obtained r value? b. Is your obtained r statistically significant (using a =.05, two tailed)? Are the Rater A and Rater B scores "reliable"? Is there good or…
12. Let (*1, 12, ., r„) be independent samples from the uniform distribution on [0,0]. Let X(n) and X(1) be the maximum and minimum order statistics respectively, (a) Find the distribution of X(m) and X(a) and hence, their means and variances. X{n) (b) Show that 2nY x where Y = – In %3D (c) Show that 2) In - Xản: Hence write a function of the geometric mean, i=1 (II GM(r) = which is Xn 1
6.2.8. Let X be N(0, 0), 0 <0 < x. (a) Find the Fisher information I(0). (b) If X₁, X2,..., Xn is a random sample from this distribution, show that the mle ofis an efficient estimator of 0. (c) What is the asymptotic distribution of √(-0)?
5. (a) Establish the formula: nroxdy = n,r,0x, Oy, + n2r20x,Oy, + n,dx,dy, + nzdx,dy2 Where dx, = x - i, dy, = 91 - y, dx, = X2 - X, dy, = y2 - y 5. (b) Find the correlation coefficient of combined sample given that %3D %3! Sample Size Mean of X Var(X) Mean of Y Correlation between X and Y Var(Y) Group 1 n = 100 i, = 80 ox? = 10 y, = 100 o = 15 %3! = 0.6 Group 2 n2 = 150 = 72 Ox = 12 y, = 118 o = 18 2 = 0.4

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1.3. Let Y₁, Y₂, ..., Yn denote a random sample of size n from a population with a uniform distribution = Y(1) = min(Y₁, Y₂, ..., Yn) as an estimator for 9. Show that on the interval (0,0). Consider is a biased estimator for 0.