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研究所、轉學考(插大)-微積分
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100年 - 100 淡江大學 轉學考 機率與微積分#55936
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1.(1) Please explain the relationship between ”Probability Theory'1 and "Statistical Inferences，’(e.g. estimation，tests，and confidence intervals).
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c. Calculate the gain for Simpson (if any). Prepare the journal entries needed by Simpson for the restructuring of the debt.
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(1) The entries to record compensation expense for 2009 and 2010.
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(2) On June 1, 2011，the vested options from 6 employees are exercised when the market price of company’ stock is $72 per share.
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(3) On December 31，2011，the vested options from the remaining 2 employees are expired.
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(2) Please explain the relationship among the concepts of limits，continuity, differentiation, and integration. You can use examples for demonstration in your explanation.
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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].
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【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
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【已刪除】4. Discuss the continuity of the following function, and indicate the points of discontinuity(if any):
#211885
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.
#211886
(1)當地冬天低於8度的機率有多大？
#211887
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