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110年 - 110 國立臺灣科技大學_碩士班招生試題_工業工程系:統計學#111373
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2. (20 points) Three balis are drawn Let X be the number of white balls selocted and Y be the nurber of black balls selected. n without replacement from 12 balls (4 white, 4 black, and 4 red).
(b) Find the probability P{Y = 1}. (5 points)
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(c) Find the conditional distribution of X, given that Y -1. (5 points)
#477112
(d) Find the probability P{X +Y≥2}. (5 points)
#477113
3. (10 points) If the joint density function of two random variables X and Y is given by f(x,y) = 2 for 0 <x≤y < 1. What is the corre. elation coefielent of X and Y?
#477114
(a) Pleme test whether the variances of the time to failure of the parts produced by different suppliers are equal, (Please clearly state the null, the alternative hypothesis, and the test statistic, and use a= 0.10) (5 pointa)
#477115
(b) The compuny has decided that if the m longer than it is for the current supplier, it will switch suppliers. Should the company switch mean time to failure for the new su uppliers is signifcantly suppliers? (Please clearly state the null, the alternat use a= 0.05) (10 points) ative bypothesis, and the test statistic, and
#477116
(a) Please construct the ANOVA table. (10 points)
#477117
(b) Please state the null and alternative bypothesis, perform the test, and state your conclusion using 0.05 level of significance. (5 pointe)
#477118
(a) Plot the least squares S prediction equation associated with two different neighborboods, and discuss your findings. (5 points)
#477119
(b) Test the overal utility of the model (Please clearly state the null, the alernative hypothesis, and the test statistic, and use a = 0.05), (5 points)
#477120
7. (10 points) Let X1,X2,..., Xn denote a a random sample from a distribution that is N(θ, 1), where the mean θ is unknown wn. Please show that there is no uniformly most powerful (UMP) test of the simple hypothesis H0 : θ= θ0, where lo be a specified value of θ, against the alternative hypothesis H1:θ≠θ0.
#477121
相關試卷
110年 - 110 國立臺灣科技大學_碩士班招生試題_工業工程系:統計學#111373
110年 · #111373
110年 - 110 國立高雄大學_碩士班招生考試_資訊工程學系:離散數學與資料結構#102139
110年 · #102139