Suppose that the elements of X = [X₁, X2, ..., Xn]' form a random sample from a Poisson (A)In(X) = //distribution where the Fisher Information about in the random sample isLet X(X) = X be an estimator of X. What influence does the sample size in the Fisher Information haveon the variation of (X)?Select one:a.A decrease in the sample size in the Fisher Information increases the variation of A(X) ►O b. A decrease in the sample size in the Fisher Information decreases the variation of (X)Oc. A decrease in the sample size in the Fisher Information has no influence on the variation ofO d. An increase in the sample size in the Fisher Information increases the variation of Â(X)of X(X)F

From cramer- rao lower bound we know that - Var(λ⏞(x)) ≥ {ψ'(θ)}2I(θ) ......(1) Where symbols have…

Answered: Suppose that the elements of X = [X₁,…

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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4. Let Y₁, Y2,..., Yn be a random sample of size 5 from a normal population with mean 0 and variance 1. Also let 15 Y = 5 i=1 following: (a) W = Y. Let Y be another independent observation from the population. Determine the distribution of the 5 ΣΥΡ i=1 (b) U = (Y-Y)². (c) R: = (d) V = i=1 √5Y6 W 2 (5Ỹ²+Y²) U
1. Let y1,.. , Yn be a random sample from a uniform distribution on the interval (0, B). Let B1 2 Li=1 Yi and B, = ) Max(y1,.., Yn) be estimators for B. Find the sampling distribution of B2 Show that B, and B, are unbiased estimators for B. 11.
1. Suppose a X value is produced by a random process that has a mean of 1 and a variance of 9, while a Y value is produced by a random process that has a mean of 9 and a variance of 1. Let Z = 3X - 2Y. Compute: a. the mean and variance of Z assuming X and X are independent. b. the mean and variance of Z assuming X and X are not independent and their correlation coefficient is 0.50.
Let X1,X2.,X, and Y1,Y2,.Yn be two random sample of size n from a normal independent distributions Var(X)=1 and Var(Y)=20?. Let U = E-1(X; – X)² and W = E1(Y; – Y)? W a. What is the sampling distribution of the statistic U + 202 b. If the 90th percentile of the statistic (U + 202 is 33.20, what is the sample size n?
2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).
The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…
The following table consists of one student athlete's time, x, (in minutes) to swim 2,500 yards and the student's heart rate, y, (beats per minute) after swimming on a random sample of 5 days: Athlete's Time (x) Heart Rate (y) x2 y? ху 33.43 145 34.89 150 35.12 125 37.27 143 36.56 138 ТОTAL 1. Compute for the value of Pearson's r. 2. Interpret the value of r.
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)?
We have a large dataset which we denote by D1, with values x1, x2, x3, ..., xN. Its mean is denoted by m. We create a new dataset D2 as follows: x1-m, x2-m, x3-m, ..., xN-m (that is, we subtract the mean from every data point). Then we create a new dataset by dividing every value in D2 by number 5. (so note that we said D2, not D1). What is the mean of D3? Group of answer choices 5 m m/5 m/ 25

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