) Let X,, X,, ..., X, be a random samplefrom the N(0, o²)-distribution, and suppose that the prior distribution for 0 is the N(H, 7²)-distribution, where o, µ and 7’ are known. Determine the posterior distribution for 6,given X,. X2, .... X,, and the optimal estimator of 0 under (i) quadratic loss, and(ii) absolute error loss.

Answered: Image /qna-images/answer/76e9f156-23f2-458b-ad61-4a9071ed034a.jpg

Answered: ) Let X, 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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(6) What will be the sampling distribution of sample total T, when samples of size n = 15 are drawn (with replacement) from the population {0, 0,0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}? The following answers are proposed. (a) The population may be viewed as B(1, ÷). So, T ~ B(15, -). (b) The population may be viewed as B(1, ). So, T ~ B(15, В(15, (c) The population may be viewed as B(1, →). So, T (d) The population may be viewed as B(17, ÷). So, T B(15, ). (e) None of the above. The correct answer is (b) (c) (d) (e) N/A (Select One)
23. A variable is described at N(5,9). This indicates normal distribution, with Mean= 5 and Variance = 9. b) a) What are the corresponding Z values for X values of 2 & 5? What is the probability that X is less than 2? What is the probability that X is less than 5? c) C: What is the probability that X is between 2 and 5? e) What is the probability that Z < -1.24? d)
To test the null hypothesis that the difference between two population proportions is equaluse StatCrunch or the formulaz =(p1 (carat) - p2 (Carat) / (Sq root) p1 (carat) (1 - p1 (carat)/n1 + p2(carat) (1 - p2(carat))/n2As long as n1 and n2 are both large, the sampling distribution of the test statistic z will beapproximately the standard normal distribution. Given the sample data below, test the claim that the proportion of female voters who plan to vote Republican at the next presidential election is less than the percentage of male voters who plan to vote Republican. Use the traditional method of hypothesis testing and use a significance level of 0.05.Men: n1 = 250, x1 = 146, p1(carat)=.584Women: n2 = 309, x2 = 103, p2(carat) = .333 3)a. Write the null and alternative hypotheses to test this claim. b. What is the value of the test statistic? Show you work.c. What is the associated P-value? d. State your conclusion and explain in context using ΅ = 0.05.
Let X₁, X₂, ..., Xn be a random sample of size n from a geometric distribution for which p is the probabil- ity of success. (a) Use the method of moments to find a point estimate for p. (b) Explain intuitively why your estimate makes good sense.
Obtain 100 (1 x)% confidence limits (for large samples) for the parameter 2 of the f(x, 2) = e-^.^* ; x ; x = 0, 1, 2,... x! Poisson distribution:
Consider again the random variable with a cumulative distribution function ofF(x) = x^2/25, for 0 ≤ x ≤ 5. (d) What is the probability of x =1? (e) Do you think x is a symmetric random variable? Why or why not? I need answers of sub-parts (d) and (e) only.
If we assume that the distribution of means is normal, then 95% of all sample means a) will fall in the interval m ± 1.96(σm) b) will fall in the interval m ± 1.645(σm) c) will be no more than 1.645(σm) from μ d) will be no more than from 1.96(σm) from μ
Let Yı, Үг, Үз, Ү4, Үş and X1, X2, ..., X, be independent and normally distributed random samples from populations with means A1 = 2 and Az = 8 and variances 12 = 5 and_a22 = k, respectively. Suppose that P(X —Ї > 10) = 0.02275, find the value of az² = k. фундука чии
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…
Let Yı, Үг, Үз, Ү4, Үş and X1, X2, ..., X, be independent and normally distributed random samples from populations with means A1 = 2 and Az = 8 and variances 12 = 5 and_a22 = k, respectively. Suppose that P(X —Ї > 10) = 0.02275, find the value of az² = k. фундука чии
For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish
7

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