O T OSuppose a random variable X is normallydistributed with mean 0 and un- knownvariance 0 > 0. That is, X - N(0,0).(a) Show that this distribution represents aregular case of the exponential class. Note:Establish both that this is from theexponential class and the regularityconditions are satisfied.(b) Given a random sample of size n fromthis distribution, construct a sufficientstatistic for the variance, 0.(c) Construct the minimum varianceunbiased estimator (MVUE) from thissufficient statistic.(d) Consider the set of hypotheses: HO : 0 =O' versus H1 : 0 < 0'. Given that this is aregular case of the exponential class ofdistributions, what is the form of thedecision rule for a Uniformly Most Powerfultest?(e) For the same hypotheses as (d) with 0' =4, if we had sample of n = 20 trials and arealized sufficient statístic v1 = = 45,20.FiltersAdd a caption.> My group

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Answered: Suppose a random variable X is normally…

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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The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)
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The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM= (round to four decimals)
Assume that the helium porosity (in percentage) of coal samples taken from anyparticular seam is normally distributed with true population variance 0.36.(a) Compute a 95% two-sided CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85. (b) How large a sample size is necessary if the width of the 95% two-sided CI is to be 0.5? (c) Compute a 98% upper one-sided CI for true average porosity of another seam based on 16 specimens with a sample average porosity of 4.56.show major intermediate steps.
1) Suppose the following model y; = B1 + u; Where is assumed to be normally distributed with mean zero and variance ơ² . Calculate analytically, following OLS technique, ß, and Var(ß,).
Suppose that you have molecular type with unknown atomic mass 0. You have an atomic scale with normally-distributed error of mean 0 and variance 0.5. (a) Suppose your prior on the atomic mass is N(80, 4). If the scale reads 85, what is your posterior pdf for the atomic mass? (b) With the same prior as in part (a), compute the smallest number of measurements needed so that the posterior variance is less than 0.01.
Show that the characteristic function of a Gaussian random variable with zero mean and variance o² is (= x (@) = exp -0² w² 2
Let S1^2 be the sampling variance for a random sample of twelve values (amount of mercury in the blood) and let S2^2 be the sampling variance for a random sample of ten values (amount of lead in the blood); samples from the same population were used. The population variance for mercury measurements is assumed to be twice the corresponding population variance for lead measurements. We will further assume that S1^2 is independent of S2^2. 1. Find a number b such that P [(S1^2/S2^2)<=b]=0.95 enter such a b to three decimal places b= 2. Consider the number b calculated above, find a number a such that P[a<=(S1^2/S2^2)<=b]=0.90 enter said a to three decimal places. a=
'Melanoma' is a form of skin cancer and each year 17% of the patients who suffer from the disease die. A random sample of 10,000 melanoma patients is formed at the start of a year. Let Y denote the number of patients in this sample who will die during the year? (a) What is the expected value of Y? That is, compute E(Y). Answer: [Select] (b) What is the variance of Y? That is, compute var(Y). Answer: [Select] (c) What is the probability that Y exceeds 1,800? That is, compute P(Y> 1,800). Answer: [Select]

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