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研究所、轉學考(插大)◆統計學
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110年 - 110 國立臺灣大學_碩士班招生考試_農業經濟研究所:統計學(E)#102206
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題組內容
4.(10%) Find the moment generating function corresponding to the following probability density functions:
(2)
其他申論題
(8) Determine a 99% confidence interval for the coefficient of x1?(3%)
#430077
(9) Using the 2.5% significance level, can you conclude that the coefficient of x2 is positive? (3%)
#430078
(10) Using the 5% significance level, test whether or not the coefficients of all independent variables in the population regression model are equal to zero. (4%)
#430079
(1)
#430080
5.(15%) Let X and Y be two independent random variables that follow a Poisson distribution with rate parameter θ and λ, respectively, i.e., X ~ Poisson(θ) and Y ~ Poisson(λ), Show that the distribution of X/(X+Y) is binomial with success probabilityθ/(θ+λ). Note: the probability density function of a Poisson distribution with rate parameter y is
#430082
(1)Find E[Y], Var[Y], and Cov(X, Y). (15%)
#430083
(2)Prove that Y/X and Xare independent. (10%)
#430084
1. Determine the mg/L of O2 required for a BOD test if 0.1 mmol of urea, (NH2)2CO, is completely oxidized into CO2, and water in a 50 ml sample. (20 points)
#430085
2. A stack gas contains carbon monoxide (CO) at a concentration of 10 % by volume. What is the concentration of CO in ug/m3? (assuming 25℃ and I atmosphere pressure) (20 points)
#430086
3. Express 10 mg/L of as CaCO3. (Mg=24, Ca=40, C=12, O=16) (20 points)
#430087
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