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110年 - 110 台灣聯合大學系統_學士班轉學生考試試題：地球物質#124783
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六、解釋名詞:
2. Pressure solution
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3. Sheeted dikes
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(a) X and Y are independent chi-square random variables with 2 and 5 degrees of freedom, respectively. What kind of distribution the random variable X+Y will be? (6%)
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(b) What is the meaning of adjusted R² for the regression analysis?(6%)
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(c) Let the variables X₁, X₂, and X₃ have the variances σ₁² = 1.0, σ₂² = 3.0, σ₃² = 5.0. Let these variables be independent and Y = 13 - 2X₁ + 3X₂ - 10X₃. Find the variance of Y.(6%)
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(d) Let Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ be a multiple regression model with X₃ =.What would be happened when we try to estimate the parameters of this model? and explainwhy? (6%)
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(e) What assumptions are usually made about the error terms of linear regression models? (6%)
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2. (10%) The annual rainfall (in inches) in a certain region is normally distributed with μ = 30, σ = 3. What is the probability that in 2 of the next 4 years the rainfall will exceed 35 inches? Assume that the rainfalls in different years are independent.
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3. (10%) If the density function of X equals Please find the value of c. What is probability for X>2 (i.e. P(X>2))?
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(a) What is the distribution of ? (5%)
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(b) If= 4, give an interval that, with 90 percent confidence, will contain the value ofXₙ₊₁. (5%)
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110年 - 110 台灣聯合大學系統_學士班轉學生考試試題：地球物質#124783
110年 · #124783
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