Motivation: Goodness of Fit Testing for a Gaussian Distribution 1 ponto possível (classificado) Let X1,..., X, be iid random variables with continuous cdf F. Let {N (μ,0²)}ER,²> denote the family of all Gaussian distributions. We want to test whether or not FE {N (1,0²)}ER,²>0 Let denote the cdf of N (#4, 2). We formulate the null and alternative hypotheses HoF H₁F = 14,0 for some μER,² > 0 for any μER,² > 0. Motivated by the Kolmogorov-Smirnov test, you define a test-statistic using the sample mean and sample variance 2: Tn sup√√F (t) | tER Assume that the null hypothesis is true. Is it true that (d) T sup B (z)| 11-00 zЄ[0,1] where B (x) is a Brownian bridge? (Refer to the slides.) True False
Motivation: Goodness of Fit Testing for a Gaussian Distribution 1 ponto possível (classificado) Let X1,..., X, be iid random variables with continuous cdf F. Let {N (μ,0²)}ER,²> denote the family of all Gaussian distributions. We want to test whether or not FE {N (1,0²)}ER,²>0 Let denote the cdf of N (#4, 2). We formulate the null and alternative hypotheses HoF H₁F = 14,0 for some μER,² > 0 for any μER,² > 0. Motivated by the Kolmogorov-Smirnov test, you define a test-statistic using the sample mean and sample variance 2: Tn sup√√F (t) | tER Assume that the null hypothesis is true. Is it true that (d) T sup B (z)| 11-00 zЄ[0,1] where B (x) is a Brownian bridge? (Refer to the slides.) True False
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 37E
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