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首頁 > 研究所、轉學考(插大)◆統計學 > 99年 - 99 國立交通大學管碩士班考試入學試題：統計學#123993 >

題組內容

2. (18分) Let X and Y have the joint density

(b) Find the marginal densities f₁(x) and f₂(y)

其他申論題

(b) f(x) = for x = 0, 1, 2, 3

(c) f(x) = for x = 3, 4, 5, 6

(d) f(x) = for x = 1, 2, 3, 4, 5

(a) Find the value of c that makes f(x, y) a probability density function.

(c) Find the conditional densities f₁(x|y) and f₂(y|x)

3. (12分) Find the mean and the variance of the uniform probability distribution given byf(x) = for x = 1, 2, 3,..., n

(a) Find the maximum likelihood estimator of λ.

(b) Is the maximum likelihood estimator unbiased?

5. (12分) In a random sample of 400 industrial accidents, it was found that 231 were due at least partially to unsafe working conditions. Please construct a 99% confidence interval for the corresponding true proportion. (Refer to the attached Tables if necessary)

6. (10分) Let the variables X₁, X₂ and X₃ have variances σ₁² = 1.0, σ₂² = 3.0 and σ₃² = 5.0. Let these variables be independent and Y = 13 - 2X₁ + 3X₂ - 10X₃. Find the variance of Y.

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