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研究所、轉學考(插大)◆工程數學
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110年 - 110 國立中山大學_碩士暨碩士專班招生考試_海下所:工程數學#104424
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1. Evaluate
for any a ＞ 0. (5%)
其他申論題
2. (20%) If the random variable X has a Poisson distribution such that P(X 1) = P(X=2). Find P(X =4).
#442067
3. (20%) Find the method-of-moments estimates for pu and σ2 based on a random sample of size n taken from an N(u,o?) distribution.
#442068
4. (20%) A random sample of size 2 is drawn from a uniform pdf defined over the interval [0,θ]. We wish to test by rejecting H0 when y1 + y2≤k. Find the value for k that gives a level of significance of 0.05.
#442069
5. (20%) Let x = (X1, X2, X3)' have a trivariate normal distribution with means 6, 4, and 2 and variance 16, 25, and 64, and with cou(X1, X2) = 6 and coc(X1,X3) = 4 and cou(X2,X3)=5. Let Y1=2X1+3X2+ X3 +2 and Y2 =4X1+ X3 +3. What is the joint distribution of y = (Y1, Y2)'?
#442070
(1) Let u1 = ＜3, 1＞, u2= ＜1, 1＞. Transform them into an orthonormal basis. (5%)
#442072
(2) Let u1 = ＜1, 1, 1＞, u2 = ＜1, 2, 2＞, u3 = ＜1, 1, 0＞ . Transform them into an orthonormal basis. (5%)
#442073
3.Let . Find a symmetric matrix B and a skew-symmetric matrix C, such that B+C=4. 1 0] (5%)
#442074
4.Solve +y=x, y(0)=3.(10%)
#442075
(1) Find L{sin(2t)}. (5%) (Write down the detailed process)
#442076
(2) Solve +3y= 13sin(2t), y(0)=6.(15%)
#442077
for any a ＞ 0. (5%) 
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for any a ＞ 0. (5%)