IT HAS BEEN FOUND THAT A FLUCTUATING ELECTRIC CURRENT X AT ONE OF THE ESKOM SUBSTATIONS HAS A UNIFORMPROBABILITY DISTRIBUTION,f(x) =a≤x≤botherwisea+b(b-a)²WITH E(X) = AND Var (X) =12AS THE STATISTICIAN AT ESKOM AND HAVE BEEN GIVEN A RANDOM SAMPLEOF 7 MEASUREMENTS X₁, X₂,,X, OF THE ELECTRIC CURRENT TO INFER ABOUT THE MEAN FLUCTUATION OVER A SPECIFICPERIOD. AFTER CAREFUL CONSIDERATION YOU HAVE IDENTIFIED THREE POSSIBLE ESTIMATORS0₁ = X₁+X7, 0₂ = X₁ +2X₂+X AND 3 = X3Show which of the estimators possess this property

Answered: Image /qna-images/answer/87b7e0b6-a78e-49bc-a15f-971b73ff6d7c.jpg

Answered: PROBABILITY DISTRIBUTION, f(x)= a+b 2…

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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Suppose that X1, . . . , Xn is a random sample from the Normal distribution N (0, σ2 ) with parameter σ > 0, Find the Maximum Likelihood Estimation of σ.
If X is a continuous random variable, what is the value of X that will be exceeded 30% of the time, ifX is uniformly distributed with a mean of 6 and a variance of 12?
A simple random sample of size n =66, is obtained from a population that is skewed left with =33 and =3. . Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?(A) Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (B) Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. (C)No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x, become approximately normal as the sample size, n, increases. (D) No. The central limit theorem…
Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each oftwo random samples selected from the same population: sample R and sample S. Let R represent a random sampleof size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal tothe point estimate obtained from S, which of the following must be true about the respective margins of errorconstructed from those samples?(A) The margin of error for S will be 4 times the margin of error for R.(B) The margin of error for S will be 2 times the margin of error for R.(C) The margin of error for S will be equal to the margin of error for R.(D) The margin of error for R will be 4 times the margin of error for S.(E) The margin of error for R will be 2 times the margin of error for S.
Let X1, X2, …, Xn be a random sample from the Normal distribution N() (a) Using method of moments to estimate the parameters and . (b) Are those estimators unbiased?
Suppose X and Y are independent random variables with the same mean µ but possibly different variances σx2 and σy2. Imagine that X and Y are the averages of independent samples of size n1 and n2, respectively, taken from populations with the same mean µ and the same variance σ2. Apply below to identify the α that minimizes and the minimum value. Be sure to simplify both the new estimator and the minimum variance. Interpret the result. The variance of αX+(1-α)Y, which also has mean µ, is minimized with α=σy2/(σX2+σy2).
If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that ni=1X2inis an unbiased estimator of σ2.
A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9(a) Find the probability of committing a type 1 error when H0H0 is true(b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms.
Let X and Y be random variables with variances Var(X) = 1 and Var(Y ) = 2. (Note that X and Y might not be independent.) What is the maximum possible value of Var(3X − 2Y + 4)?
Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X = Y + c for some constant c almost surely. Also find the value of c.
The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…

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