Suppose Y₁, Y2,…, Yn is an iid sample from a beta (a, ß) distribution with a = ß = 0, 0 > 0a. Use the Factorization Theorem to show thatnT = []Y;(1 — Y;)i=1is a sufficient statistic.b. The sample variancen1=ΣΥ; - Y)2n1i=1is an unbiased estimator of the population variance14(20 + 1)*Is S² the MVUE of o2? Explain.

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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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Consider the performance function Y= 2X1-2X2+8X3 are all normally distributed random variables with μΧ1 = 10.4 ; μΧ2 = 11.8 ; μΧ3= 11.5Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 % X1 X2 X3q = 1 0,8 6 X1 0,8 1 0,5 X2 -----> correlation of Matrix 0,6 0,5 1 X3 Y < 0; failure occurs 15 simulations Pf =? . Determine the probability of failure ? (Reliability of Structures)
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suppose that 43% of people who enter a store will make a purchase. Random samples of people who walk into a particular store is studied, and the proportion of those who made a purchase is found for each sample. Assume that all the samples were the same size. If 29.46% of all sample proportions are less than 0.3274. What was the z-score for 0.3274? What is σp′?
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Before the furniture store began its ad campaign, it averaged 200 customers per day. The manager is investigating if the average is larger since the ad came out. The data for the 16 randomly selected days since the ad campaign began is shown below: 209, 193, 187, 205, 209, 218, 211, 223, 229, 199, 207, 209, 207, 210, 202, 233 Assuming that the distribution is normal, what can be concluded at the α = 0.10 level of significance? The test statistic = ______________ (please show your answer to 3 decimal places.)
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
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Suppose that we would like to test the following hypotheses on the population correlation coefficient ρ: H0: ρ ≤ 0 and H1: ρ > 0. The sample correlation coefficient (r) for a sample with 7 observations (n = 7) on x and y is 0.35 . Then the test statistic t has a value of

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Suppose Y₁, Y2,..., Yn is an iid sample from a beta (a, 3) distribution with a = 3 = 0,0 >0 a. Use the Factorization Theorem to show that n T = ∙ II Y¿(¹ — Y;) i=1 is a sufficient statistic.