问答题已知A=(α 1 ，α 2 ，α 3 ，α 4 )是4阶矩阵，α 1 ，α 2 ，α 3 ，α 4 是4维列向量，若方程组Ax=β的通解是(1，2，2，1) T +k(1，-2，4，0) T ，又B=(α 3 ，α 2 ，α 1 ，β-α 4 )，求方程组Bx=α 1 -α 2 的通解．

问答题设函数f(x)连续可导，且f(0)=0，，求

问答题确定如下无穷小的阶n：

问答题X，Y的联合概率密度函数为f(x，y)=，(λ＞0)．

问答题求

问答题设连续函数f(x)满足方程求f(x)的表达式．

问答题已知(X，Y)的联合概率密度为

问答题计算

问答题设随机变量X服从二项分布B(n，p)，随机变量Y为求：(1)Y的概率分布；(2)Y的期望EY与方差DY．

问答题设f(x)为连续函数，证明：

问答题已知4阶方阵A=[α 1 ，α 2 ，α 3 ，α 4 ]，α 1 ，α 2 ，α 3 ，α 4 均为4维列向量，其中α 2 ，α 3 ，α 4 线性无关，α 1 =2α 2 -α 3 ，如果β=α 1 +α 2 +α 3 +α 4 ，求线性方程组AX=β的通解．

问答题二次型，经正交变换化为标准形．(Ⅰ)求a，t的值；(Ⅱ)求所用的正交变换X=PY．

问答题You've had a problem, you've thought about it till you were tired, forgotten it and perhaps slept on it, and then flash! When you weren't thinking about it suddenly the answer has come to you, as a gift from the gods. Of course all ideas don't come like that, but the interesting thing is that so many do, particularly the most important ones. They burst into the mind, glowing with the heat of creation. How they do is a mystery. (46) Psychology does not yet understand even the ordinary process of conscious thought, but the emergence of new ideas by a "leap in thought" is particularly intriguing, because they must have come from the somewhere. For the moment let us assume that they come from the "unconscious". (47)This is reasonable, for the psychologists use this term to describe mental processes which are unknown to the subject, and creative thought consists precisely in what was unknown becoming known. (48) It seems that all truly creative activity depends in some degree on these signals from the unconscious, and the more highly intuitive the person, the sharper and more dramatic the signals become. But growth requires a seed, and the heart of the creative process lies in the production of the original fertile nucleus from which growth can proceed. (49) This initial step in all creation consists in the establishment of a new unity from disparate elements, of order out of disorder, of shape from what was formless. The mind achieves this by the plastic reshaping, so derived from a new unit, of a selection of the separate elements derived from experience and stored in memory. Intuitions arise from richly unified experience. (50) This process of the establishment of new form must occur in pattern of nervous activity in the brain, lying below the threshold of consciousness, which interacts and combines to form more comprehensive patterns. Experimental physiology has not yet identified this process, for its methods are as yet insufficiently refined, but it may be significant that a quarter of the total bodily consumption of energy during sleep goes to the brain, even when the sense organ are at rest, to maintain the activity of ten thousand million brain cells. These cells, acting together as a single organ, achieve the miracle of the production of new patterns of thought. No calculating machine can do that, for such machines can "only do what we know how to design them to do", and these formative brain processes obey laws which are still unknown. Can any practical conclusions be drawn from the experience of genius? Is there an art of thought for the ordinary person? Certainly there is no single road to success; in the world of the imagination each has to find his own way to use his own gift.

问答题求积分，D：|x|≤1，0≤y≤2．

问答题设随机变量X与Y相互独立，均服从参数为1的指数分布．记Z1=min(X，Y)和Z2=max(X，Y)．试求 (Ⅰ)Z1和Z2的密度函数f1(z)和f2(z)； (Ⅱ)求EZ1和EZ2．