(a) What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 3 or 5? (10 %)

二、假設 \(X_1\)、\(X_2\)、\(X_3\) 為三個獨立的常態分配，其平均數分別為 \(\mu_1\)、\(\mu_2\)、\(\mu_3\)，且其變異數均為未知的 \(\sigma^2\)。在顯著水準 \(\alpha = 0.05\) 下，想檢定 \(H_0: \mu_1 = \mu_2 = \mu_3\)。若從 \(X_1\)、\(X_2\)、\(X_3\) 分配中各抽出的樣本數分別為 \(n_1 = 5\)、\(n_2 = 3\)、\(n_3 = 4\)，且觀測值如下：試以此資料檢定欲接受或棄却 \(H_0\) ? (10 分)\((\sum x_{1j} = 58\), \(\sum x_{2j} = 34\), \(\sum x_{3j} = 50\), \(\sum \sum x_{ij}^2 = 1734\), \(F_{0.05}(2,9) = 4.26\), \(F_{0.025}(2,9) =\)5.71), \(F_{0.05}(3,12) = 3.49\), \(F_{0.025}(3,12) = 4.47\)

題組內容

(a) What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 3 or 5? (10 %)

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