Let X1, X2, ..., X, be a random sample from a normal distribution with mean µ andvariance o?.(a) Find an unbiased estimator for o?.( b) Show that Σ(x-Χ? Σ (Χ )- nX.i=1i=1(c) Find an estimator for o? using the method of moments. Is this estimator bi-ased/unbiased? Is it consistent?

Answered: Let X1, X2, . .., X, be a random sample…

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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Use the following data to answer question 8 - 12. A number of studies have claimed evidence that the first-born in a family is, on the whole, more likely to be "successful" than later-borns. A study along this direction compared the IQs of a random sample of 80 first-borns with those of an independent random sample of 105 later-borns. The data are summarized below: Sample size Sample mean Sample SD First-borns 80 112 7.2 Later-borns 105 108 8.0
You need to test whether the average mealtime spending of American tourists (population 1) is greater than that for British tourists (population 2). Assume that you have a sample of n1=7 with sample mean X1=40 and a sample standard deviation of S1=6, and you have an independent sample of n2=16 from another population with a sample mean of X2=31 and sample standard deviation S2=5. Complete parts (a) to (d). Click here to view page 1 of the table of the critical values of t. LOADING... Click here to view page 2 of the table of the critical values of t. LOADING... a. What is the value of the pooled-variance t test statistic for testing? t=enter your response here (Type an integer or a decimal rounded to two decimal places as needed.) b. In finding the critical value of the test statistic t, how many degrees of freedom are there? There are enter your response here degrees of freedom. c. Using a significance level of α=0.01, what is the critical value for a…
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This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function 1 p(x) = e (x - 1)?/(202), V 2n 0 where n = 3.14159265... and o and u are constants called the standard deviation and the mean, respectively. Its graph (for o = 1 and u = 2) is shown in the figure. f(x) 0.3 0.2 0.1 3 4 5 With o = 3 and u = 0, approximate p(x) dx. (Round your answer to four decimal places.)
Show that the estimates βˆ1 = 1.572 and βˆ2 = 1.357 used in the first experiment ofTable 3.1 are in fact the OLS estimators. note:table 3.1 is uploaded in jpg
A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is p = 60, find the z-score for this sample: If it was obtained from a population with o = 16 Z = If it was obtained from a population with o = 32 Z = If it was obtained from a population with o = 48 Z =
answer the following question number 3 with all parts
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The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?
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1. You are interested in the effect of a new learning technique. The performance score on the test before applying the new learning technique is 50 (u=50), the standard deviation is 4 (o=4). You obtained a sample of 64 subjects and applied the new learning technique. After that, their performance score on the test increased by 2 (x=52). Did the new learning technique improve/had any effect on the performance? The answer, using 4 steps of hypothesis testing. Please use APA style to report your result. Assume that a-level=.05 2. You are interested in the effect of a new learning technique. The performance score on the test before applying the new learning technique is 50 (u=50), the standard deviation is 24 (o=24). You obtained a sample of 64 subjects and applied the new learning technique. After that, their performance score on the test increased by 2 (x=52). Did the new learning technique improve/had any effect on the performance? The answer, using 4 steps of hypothesis testing.…
Example 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 45, and (iii) |X – 30l > 5.

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