3. A bivariate population of (X,Y) is sampled independently on three occasions. On the first, arandom sample of size no is taken and only T = min{X,Y} is observed for each pair. On thesecond, a random sample of size nį is taken, and only the X-marginal is observed for each pair.Finally, a random sample of size n2 is taken, and only the Y-marginal is observed for each pair.Therefore, the combined set of observations is of the form (T, X, Y), where T =X = (X1,..., Xn1) and Ymodel for (X, Y):(T1,...,Tno),(Y1, ..., Yn2). Assume the following two-parameter probabilityP(X > x,Y > y) = expx > 0, y > 0, 0 > 0, 0 < 8 < 1 with unknown parameters 0 and 8.(a) Present the joint pdf of (T, X, Y).(b) Is the above family an exponential family? Justify your answer.

denote a bivariate population that is sampled independently on occasions.The random sample size…

Answered: 3. A bivariate population of (X,Y) is…

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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If we let X1, X2,...Xn be a random sample from the distribution N( μx = 8, σx = 4), then what would the distribution of (X-8)/(4/√n) be? If we let X1, X2,...X10 be a random sample from the distribution N( μ, σ), then what is the value k so that P( (X-μ)/(σ/√10) < k ) = .05?
A survey was conducted of newlyweds in a country who have a spouse of a different race or ethnicity from their own. The survey included random samples of 1000 newlyweds in Ethnicity A and 1000 newlyweds in Ethnicity B. In the survey, 14% of respondents in Ethnicity A and 21% of respondents in Ethnicity B had a spouse of a different race or ethnicity from their own. At α = 0.01, is there evidence to support the claim that the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own is less than the proportion of newlyweds in Ethnicity B that have a spouse of a different race or ethnicity from their own? Let p₁ represent the proportion of newlyweds in Ethnicity A who have a spouse of a different race or ethnicity from their own. Let p2 represent the proportion of newlyweds in Ethnicity B that have a spouse of a different race or ethnicity from their own. State the null and alternative hypotheses. A. Ho: P₁ P2 B. Ho: P₁ P2 Ha: P₁ P2 OC. Ho:…
Suppose Y₁,..., Yn are independent random variables each with the Pareto distribution and E(Y) = (Bo + B1Xi) Is this a generalized linear model with a canonical link? Give reasons for your answer.
9) Find L3.2 (5) using the nodes xo = 3,x1 = 4, x2 = 6 ,x3 = 8 %3D
8) Consider the data (1,1), (3,9), (4,16), If f[1,3] = 4, f[3,4] = z, f[1,3,4] 1. find z %3D
What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y optimal time in hours. A random sample of divers gave the following data. 15.1 23.3 32.2 38.3 51.3 20.5 22.7 2.48 2.38 1.48 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Roundr to three decimal places.) Ex = 203.4 Ey = 12.7 Ex2 = 0.001 Ey? = 0.002 Exy = 931.638 r= -0.9655 (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t = -8.29 critical t = -3.36 Conclusion O Reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient evidence that p < 0. Fail to reject the null hypothesis. There is…
Question 3. Let X₁,, Xn be a random sample from a distribution with the pdf given by f₁₁x(x) = exp(-ª) if x ≥ A, otherwise f(x) = 0, where > 0. Find the MLE's of 0 and X. Start by writing the likelihood function and note the constraint involving A. Question 4. #4.2.9 of the textbook.
An electrochemical engineer has manufactured a new type of fuel cell (a type of battery)which has to undergo testing to prove its duration: the time it takes to go from fullycharged to completely uncharged, under a fixed nominal load. From the computational simulation models she has, the variance of the duration is σ2 = 4 h2 (hours squared)but she wants to estimate the mean duration time μ. To achieve this she is determinedto do the tests multiple times in independent but identical conditions. Can you findwhat is the smallest number of these tests that she has to do in order for her estimatedmean duration to be within ±0.2 h tolerance of the true mean with 95% certainty

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