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研究所、轉學考(插大)◆工程數學
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110年 - 110 國立中央大學_碩士班招生考試_通訊工程學系/不分組(一般生)：工程數學#105325
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題組內容
5.(8%) A box contains 10 identical balls numbered 1 through 10. Suppose 3 balls are drawn in succession.
(a)(4%) Find the probability that the smallest number drawn is more than or equal to 4.
其他申論題
(a) (5%) Use the Gram-Schmidt process to find an orthonormal basis for the column space of A.
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(b) (7%) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular.
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(c) (8%) Solve the least squares problem Ax = b
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4. (10%) Consider the matrixwith parameter x. Specify all numbers x, if any, for which A is positive definite. Explain your answer.
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(b)(4%) Find the probability that 8 is the largest number drawn.
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6.(8%) We have three coins; the first two coins are fair and the last coin is two-headed. We pick one of the coins at random, and toss it twice. Heads show both times. Find the probability that the coin picked is fair.
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7.(8%) The random variable x is uniform in the interval [-5, 5]. Find C.D.F. Fy(y) and p.d.f. fy(y).
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8.(10%) The joint p.df. of x and y for some k. Deter- mine the conditional p.d.f.
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(a)(8%) Determine the joint p.d.f. of z and w.
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(b)(8%) Find the p.d.f. fz(z) and fw(w). Are z and w independent random variables?
#447125
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