Let X1 be the sample mean of a random sample of size n from a Normal(µ, o7) population and X2 be the sample mcan of a random sample of the same size n from a Normal(4, o) population and the two samples are independent. Note that the two samples have the same population Imean ți but o o. Let i = wX1 +(1 – w)X2,0

Let X1 be the sample mean of a random sample of size n from a Normal(µ, o7) population and X2 be the sample mcan of a random sample of the same size n from a Normal(4, o) population and the two samples are independent. Note that the two samples have the same population Imean ți but o o. Let i = wX1 +(1 – w)X2,0

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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2. Let Y₁, Y₂, Y3, Y4, Y5 and X₁, X₂, ..., X, be independent and normally distributed random samples from populations with means μ₁ = 2 and μ₂ = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Ỹ > 10) = 0.02275, find the value of 0₂² = k. (5) Suppose that Y. Y y and X. X. X are independent normally distributed random
2. Let X₁,..., Xn be iid observations from a pdf defined by 0 f(x|0) = 0 0. (1+x)¹+0¹ Find a complete sufficient statistic.
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The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 94% level and we use a normal critical value, then what critical value should we use? i) Calculate a 94% confidence interval(using a normal critical value) for μ.
A random sample of n1 = 20 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 11. For Englewood (a suburb of Denver), a random sample of n2 = 10 winter days gave a sample mean pollution index of x2 = 31. Previous studies show that σ2 = 18. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 < μ2; H1: μ1 = μ2H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 = μ2; H1: μ1 < μ2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population…
Let X1, X2,...X, be a random sample from f(x,e) = -.0 < x< 8, then T= max(X,} is a %3D complete statistic for the parameter 0 Select one: O True False
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Let X1,X2.,X, and Y1,Y2,.Yn be two random sample of size n from a normal independent distributions Var(X)=1 and Var(Y)=20?. Let U = E-1(X; – X)² and W = E1(Y; – Y)? W a. What is the sampling distribution of the statistic U + 202 b. If the 90th percentile of the statistic (U + 202 is 33.20, what is the sample size n?
Let X1,X2,...,X25 be a random sample from N(u,36). Find UMPT of size a = 0.05 for testing HoH = 27 vs H,iH<27
Q3. Generate three random variates according to each of the following distributions using your own uniform random variates from U(0, 1) and list them: • Discrete Uniform: U (15, 17) • Uniform: U (0.57, 1.5). • Triangular: Triang (2, 10, 4). • Binomial: Bin (12, 0.4). • Lognormal: LN (5, 1). Beta: Beta (5, 5). • Negbin (8, 0.4) • Weibull (.5, 2.5) Geom (0.5) • PT5 (0.5, 0.5)
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