Suppose that Y₁, Y₂ , . . . , Yn denote a random sample of size n from a normal dis-tribution with mean µ and variance 1. Consider the first observation Y₁ as an estimatorfor μ.a. Show that Y₁ is an unbiased estimator for u.b. Find P(|Y₁ − µ|) ≤ 1c. Based on the result of part (b), is Y₁ a consistent estimator for u?

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Answered: 2 Suppose that 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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4) A set of measurements is given as follows. X = [0.1, 0.3, 0.8, 12,4, 7,9] We want to approximate the source of this data with Gamma distribution, i.e., X~Gamma(a, B). For Gamma distribution, the mean and variance can be found from the below equations. a Hx a o = Find the parameters of Gamma distribution to fit the data. Come up with two other distributions that you think are good representation of this data. Justify your answer.
A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 70 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev SE Mean Men Women 98% CI for mu Men - mu Women (- 12.20, - 1.00) T-Test mu Men = mu Women (vs H2 O C. Ho: H1 = H2; Ha: H1 #H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value? P-value =
1/7.dO 14 Juel If X is random variable with parameter mean = 3 variance = 9 find 7... Find P(x> 0) 0.8413.a C 0.5 0.99 .c 0.4.d C
A company manufactures tonnis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.7 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between -to ak and t as then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.8 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -th os and to 96- -to.96 = 0.96 = (Round to three decimal places as needed.)
A scientist studying babies born prematurely would like to obtain a n estimate for the mean birth weight.
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).
7. Assume that X and Y have a bivariate normal distribution having means 14.l and 1.3, and standard deviations 2.5 and 0.1, respectively, with correlation coefficient 0.8. Find P(Y >1.4|X =15) and P(X >15|Y = 1.4).
Answer last 3 parts. t hank y o u.
A large airline company called Fusion Fly monitors customer satisfaction by asking customers to rate their experience as a 1, 2, 3, 4, or 5, where a rating of 1 means "very poor" and 5 means "very good". The customers' ratings have a population mean of u=3.25, with a population standard deviation of o=1.86. Suppose that we will take a random sample of n=8 customers' ratings. Let x represent the sample mean of the 8 customers' ratings. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find u- (the mean of the sampling distribution of the sample mean). (b) Find o- (the standard deviation of the sampling distribution of the sample mean).
pls. answer using 7 steps:-Parameter of interest-Null hypothesisAlternative hypothesis -Test statistic -Reject H0 if: -Computations: -Conclusion
Number...2
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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