3. Suppose Y₂ is an i.i.d sequences of random variables, such as Y; ~ N(0, 1) for i=1,..., n. Let us consider the following estimators:n(a) Determine the mean of the estimators;(b) Determine the variance of the estimators;(c) Are the estimators biased?82=2(31-1(y₁ + Yn)

Yi follows iid N(θ, 1) We have to find a..Mean of given estimators b...Variances of estimators…

Answered: = 3. Suppose Y is an i.i.d sequences of…

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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7. For the following data: 9, 5, 10, 7, 9, 10, 11, 8, 12, 7, 6, 91. Compute the z-score for the raw score of 10.2. Compute the z-score for x = 6. 8. Find the probabilities for the following z-scores:1. p(z < 0.50)2. p(z > -0.25)3. p(z < -1.35)4. p(z > 1.68) 9. Given a distribution with ? = 225 and ? = 15, find the following probabilities:1. p(X > 227)2. p(X > 212)3. p(X < 230)4. p(X < 220)
. Given a normal random variable X with mean μ = 100 and variance o² = 49 if we randomly observe X=30, is this an unusual observation? (a) This would be an unusual observation because it lies less than 3 standard deviations away from the mean. (b) This would not be an unusual observation because it lies less than 3 standard deviations away from the mean. (c) This would be an unusual observation because it lies more than 3 standard deviations away from the mean. (d) This would not be an unusual observation because it lies more than 3 standard deviations away from the mean.
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: �"!= 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4.What is the variance of � "!
Suppose X1,., Xn, for n > 1, are sampled independently from a distribution with mean u and variance o?. Consider the following four estimators for X1+ Xn 2 X1 2 п(п + 1) i=1 a. Calculate the bias of each of these estimators. b. Calculate the standard error for each estimator. c. Which estimator would you choose to use? (Give a reason for your choice).
13. Answer the following for the probability distribution 1 f(x) = (2x + 1) (2x + 1) X= 0, 1, 2, 3 16 a. Find the mean and the variance. μ = b. EX²-4X+6) 0²=
Please solve (a) & (b) only! Thanks.
1. Six batteries taken at random from a large lot were subjected to life tests with the following results: 19, 22, 18, 16, 25, and 20 hours. Find the probability that the sample mean of x= 20 hours, as observed here, or one less than 20 hours could arise if the true mean of the lot of batteries is 21.5 hours, assuming a known variance of o = 10 hours, for the individual batteries in the lot. %3D
34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.

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= 3. Suppose Y is an i.i.d sequences of random variables, such as Y₂~ N(0, 1) for i 1,..., n. Let us consider the following estimators: 0₁ n- Yi, (a) Determine the mean of the estimators; (b) Determine the variance of the estimators; (c) Are the estimators biased? 1 6₂ = (3₁+ Yn)