100年 - 100 淡江大學 轉學考 機率與微積分#55936

科目：研究所、轉學考(插大)-微積分 | 年份：100年 | 選擇題數：0 | 申論題數：6

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所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (6)

1.(1) Please explain the relationship between ”Probability Theory'1 and "Statistical Inferences，’(e.g. estimation，tests，and confidence intervals).
(2) Please explain the relationship among the concepts of limits，continuity, differentiation, and integration. You can use examples for demonstration in your explanation.
2. If the random variable X is the outcome of throwing a fair dice，then the sample space of X is { 1， 2，3, 4，5, 6}. Please use Riemann-Stieltjes integral to calculate the expectation and variance of X, that is，E[X] andVar[X].
【已刪除】3. Please find the density function of the new random variable W= | X |，where X is a random variable following the t distribution with n degrees of freedom，and has the following density function :Hint: Γ(m) is the gamma function 
【已刪除】4. Discuss the continuity of the following function, and indicate the points of discontinuity(if any):
5. Find the Taylor's expansion of the function f(x) = log(l + x) at x = 0. Please show at least the first four terms of the Taylor’s expansion.