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研究所、轉學考(插大)◆工程數學
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108年 - 108 國立臺灣大學_碩士班招生考試：工程數學(D)#124907
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題組內容
3. Let T be a linear operator on R3 such that
(a) (4%) Find T
.
其他申論題
(a) (6%) Find all the eigenvalues of A.
#531191
(b) (6%) Find an orthonormal basis for R3, consisting of the eigenvectors of A.
#531192
(c) (6%) Find , where e1 = .
#531193
(d) (2%) Find the nullity of A.
#531194
(b) (6%) Find T
#531196
(a) What is the mathematical definition of a RV? (3%)
#531197
(b) What is the mathematical definition of a probability function? (3%)
#531198
(c) Consider the experiment of throwing a fair 2-sided dice, where the sample space S = {?, ?} and Prob({?}) = Prob({?}) = 0.5. Define a random variable X for this experiment and write down the probability mass function PMF of X, i.e., Prob(X=x) for all real x ∈ R. (5%)
#531199
(a) You know that the previous taxi arrival is s time ago. Let TR be the remaining time you have to wait for the next taxi arrival. Derive the probability that you will need to wait for no more than a time duration r, knowing that the previous arrival was s time ago. (You need to give the derivation, not just the answer. 10%)
#531200
(b) Now (time 0), you decide not to take a taxi but to count the number of taxi arrivals in a period [0, τ]. Let the number of arrivals in [0, τ] be K, which is a RV. Derive Prob(K = 0). (You need to give the derivation, not just the answer. 5%)
#531201
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