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!! I need only (d) (e) (g)! !!! In this project, we want to estimate the...
Suppose we want to estimate a parameter θ of a certain distribution and we have the following independent point estimates N(0+0.1,0.01) N(0, 0.04) B2 ~ a) What are the mean square errors for these point estimates? (4pts) b) Find a point estimate with mean square error less than or equal to 0.01. (2pts) c) Only use ël and Ộ2, find the unbiased estimator with the smallest variance possible. What is that estimator? What is the smallest variance? (6pts) Suppose we...
Problem 2. (26 points) Two random variables X and Y are jointly normally distributed, with E(X)x, EY) y and co-variance Cov(X,Y) = ơXY. To estimate the population co-variance ơXY, a very simple random sample is drawn from the population. This random sample consists of n pairs of random variables {OG, Yİ), (XyW), , (x,,y,)). Based on the sample, we construct sample co-variance SXY as: Ti-1 2-1 1. (4 points) Show Σ(Xi-X) (Yi-Y) = Σ Xix-n-X-Y. 2. (4 points) Find E(Xi...
Now if I estimate y using both Xi and X, which estimator is better in terms of efficiency? (3] 3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be u2. However, you do not know the value of , so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume...
3. In a Monte Carlo method to estimate T, we draw n points uniformly on the unit square [0, 1]2 and count how many points X fall inside the unit circle. We then multiply this number by 4 and divide by n to find an estimator of T (a) What is the probability distribution of X? b) What is the approximate distribution of 4X/n for large n? (c) For n- 1000, suppose we observed 756 points inside the unit circle....
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n. Let B 1 be the OLS estimator for B 1. Which statement is the most irrelevant to the consistency of B1? Hint: see Lecture Note 2 (p.25-p.28) a. When n is large, the estimator B 1 is near the population parameter B1 O". Consistency of B1 is mathematically written as B1-B1 VB) is inversely proportional to the sample size n. Od. RMSE is close...
I am looking for a solution for question number 2 ONLY with steps please, so I can find my mistake. 1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cov (Xi. Ui)s 0, E [Xn] = 0 and E [x?] = 1 . Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions 2. Assume the structural equation...
18. Supppse(Xy, n 1) are iid with E(%)--0, and E(X )-1. Set S,- Li i-1 Xi. Show Sn →0 n1/2 log n almost surely. 18. Supppse(Xy, n 1) are iid with E(%)--0, and E(X )-1. Set S,- Li i-1 Xi. Show Sn →0 n1/2 log n almost surely.
why is this wrong for vectors vector<char> decrypt{ {'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A'}, {'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B'}, }; for(int...
Y(z) c(t), C(s) r(t), R(S) + - et), E(S) E*(s), Ez To- D(z) G (s) = (1-e-STºys H(s) 32. If the system above has Y(z)R(z)= 1+z), and if the input is the unit step r(t)=u(t), then the signal y[n]= u[n]-e-Tou[n-1) | u[n]+u[n-1] a) c) u[n] + u[n-1) d) none above 33. If the system above has Y(z)/R(z)= 1+z), the dc gain of the system is C(z)/R(z)= b) 1/2 c)2 d) none above a) o 34. If the system above has...
How to do (d) and (e)? Thanks. 11. Let X, X1, X2, ... be independent and identically distributed random variables taking values 0, 1, 2 with px(0) = 1, px(1) = 3 and px(2) = 1. Define Sn X1 Xn, n > 1. (a) Compute the probability generating function of X (b) Find the probability generating function of Sp. 2) from the probability generating function (c) Find P(Sn (d) Derive the moment generating function of S from its probability generating...