最新2016年电大应用概率统计试题考试小抄.doc

应用数学一、填空题 （每小题3分，共21分）1已知则2设且则3已知随机变量在0，5内服从均匀分布，则4设袋中有5个黑球、3个白球，现从中随机地摸出4个，则其中恰有3个白球的概率为 . 5设是来自正态总体的一个样本，则6有交互作用的正交试验中，设与皆为三水平因子，且有交互作用，则的自由度为 .7在MINITAB菜单下操作，选择可用来讨论 的问题，输出结果尾概率为，给定，可做出 的判断.二、单项选择题（每小题3分，共15分）1设为两随机事件，则结论正确的是（ ） （A）独立 （B）互斥 （C） （D）2. 设与分别为随机变量与的分布函数.为使是某一随机变量的分布函数，在下列给定的各组数值中应取（ ） （A）（B）（C）（D）3设和分别来自两个正态总体与的样本，且相互独立，与分别是两个样本的方差，则服从的统计量为（ ） （A） （B） （C） （D）4. 设关于的线性回归方程为则、的值分别为（ ） （） （A）8.8，-2.4 （B）-2.4，8.8 （C）-1.2，4.4（D）4.4，1.2 5若分布，则服从（ ）分布.（A）（B）（C）（D）四、计算题（共56分）1据以往资料表明，某一3口之家，患某种传染病的概率有以下规律： P孩子得病=0.6 ，P母亲得病 | 孩子得病=0.5 ，P父亲得病 | 母亲及孩子得病=0.4 ，求母亲及孩子得病但父亲未得病的概率.（8分）2.一学生接连参加同一课程的两次考试.第一次及格的概率为0.6，若第一次及格则第二次及格的概率也为0.6；若第一次不及格则第二次及格的概率为0.3.（1）若至少有一次及格则能取得某种资格，求他取得该资格的概率？（2）若已知他第二次已经及格，求他第一次及格的概率？（12分） 3假定连续型随机变量的概率密度为，求（1）常数，数学期望，方差；（2）的概率密度函数.（12分）4. 某工厂采用新法处理废水，对处理后的水测量所含某种有毒物质的浓度，得到10个数据（单位：mg/L）: 22 , 14 , 17 , 13 , 21 , 16 , 15 , 16 , 19 , 18而以往用老办法处理废水后，该种有毒物质的平均浓度为19.问新法是否比老法效果好？假设检验水平，有毒物质浓度.（12分）（）5. 在某橡胶配方中，考虑三种不同的促进剂（A），四种不同份量的氧化锌（B），每种配方各做一次试验，测得300%定强如下：定强氧化锌促进剂B1B2B3B4A1 31343539A233363738A335373942试检验促进剂、氧化锌对定强有无显著的影响？（12分）()四. 综合实验报告（8分）052应用数学一、 填空题（每小题2分，共26=12分）1、设一维连续型随机变量X服从指数分布且具有方差4，那么X的概率密度 函数为： 。2、设一维连续型随机变量X的分布函数为， 则随机变量的概率密度函数为： 。3、设总体X服从正态分布，它的一个容量为100的样本的均值服从正态分布 。4、设是参数的估计量，若 成立，则称是的无偏估计量。5、在无交互作用的双因素试验的方差分析中，若因素A有三个水平，因素B有四个水平，则误差平方和SSE的自由度 。6、设关于随机变量Y与X的线性回归方程为，则。 （ ）二、单项选择题（每小题2分，共26=12分）1、 设相互独立的两个随机变量X、Y具有同一分布，且X的分布律为： 则随机变量的分布律为（ ） 2、若随机变量X的数学期望E（X）存在，则（ ） 3、设X为随机变量，下列哪个是X的3阶中心矩？（ ） 4、设两总体，且未知，从X中抽取一容量为的样本，从Y中抽取一容量为的样本，对检验水平，检验假设： 由样本计算出来的统计量的观察值应与下列哪个临界值作比较？（ ）5、在对回归方程的统计检验中，F检验法所用的统计量是：（ ） （其中SSR是回归平方和，SSE是剩余平方和，是观察值的个数）6、设总体，从X中抽取一容量为的样本，样本均值为，则统计量服从什么分布？（ ） 三、判别题（每小题2分，共26=12分）（请在你认为对的小题对应的括号内打“”，否则打“”）1、设A、B是两个随机事件，则 （ ）2、设是服从正态分布的随机变量的分布函数，则 （ ）3、相关系数为零的两个随机变量是相互独立的。 （ ）4、如果X、Y是两个相互独立的随机变量，则 （ ）5、若两随机变量具有双曲线类型的回归关系，则可作适当的变量代换转化为线性回归关系。（ ） 6、用MINITAB软件做有交互作用的双因素试验的方差分析时可在菜单中选择： （ ） 四、计算题（每小题8分，共87=56分）1、 一射手对同一目标独立进行四次射击，若至少命中一次的概率为，（1） 求该射手的命中率；（2） 求四次射击中恰好命中二次的概率。2、 如下图，某人从A点出发，随意沿四条路线之一前进，当他到达B1，B2，B3，B4 中的任一点时，在前进方向的各路线中再随意选择一条继续行进。（1） 求此人能抵达C点的概率；（2） 若此人抵达了C点，求他经过点B1的概率。B4AB1B2B3C 3、某公共汽车站从早上6时起每隔15分钟开出一趟班车，假定某人在6点以后到达车站的时刻是随机的，所以有理由认为他等候乘车的时间X服从均匀分布，其密度函数为： ，求（1） 此人等车时间少于5分钟的概率；此人的平均等车时间E（X）。 4、 设二维随机变量（X，Y）的联合密度函数为（1）判断X与Y是否相互独立；（2）求概率5、设某种清漆9个样本的干燥时间（单位：h）分别为6.0，5.7，5.8，6.5，7.0，6.3，5.6，6.1，5.0，设干燥时间总体服从正态分布，求平均干燥 时间的置信度为0.95的置信区间。 （）6、 某种导线，要求其电阻的标准差不得超过,今在生产的一批导线中取样品9根，测得，设总体为正态分布，问在水平下能否认为这批导线的标准差显著地偏大？ （） 7、 有三台机床生产某种产品，观察各台机床五天的产量，由样本观察值算出组间平方和，误差平方和，总离差平方和，试问三台机床生产的产品产量间的差异在检验水平下是否有统计意义？（）五、综合实验（本题8分，开卷，解答另附于数学实验报告中）062应用数学一、 填空题（每小题2分，共26=12分）1、设服从01分布的一维离散型随机变量X的分布律是：， 若X的方差是，则P=_。2、设一维连续型随机变量X服从正态分布，则随机变量 的概率密度函数为_。3、设二维离散型随机变量X、Y的联合分布律为：则a, b满足条件：_。4、设总体X服从正态分布 ， 是它的一个样本，则样本均值的方差是_。5、假设正态总体的方差未知，对总体均值 m 作区间估计。现抽取了一个容量为n的样本，以表示样本均值，S表示样本均方差，则m 的置信度为1-a 的置信区间为：_。6、求随机变量Y与X的线性回归方程，在计算公式 中，。二、单项选择题（每小题2分，共26=12分）1、设A，B是两个随机事件，则必有（ ）2、设A，B是两个随机事件， 则（ ）3、设X，Y为相互独立的两个随机变量，则下列不正确的结论是（ ）4、设两总体未知，从X中抽取一容量为的样本，从Y中抽取一容量为的样本，作假设检验：所用统计量 服从（ ）5、在对一元线性回归方程的统计检验中，回归平方和SSR的自由度是：（ ） 6、设总体，从X中抽取一容量为的样本，样本均值为，则统计量服从什么分布？（ ） 三、判别题（每小题2分，共26=12分）（请在你认为对的小题对应的括号内打“”，否则打“”）1、（ ）设随机变量X的概率密度为，随机变量Y的概率密度为，则二维随机变量（X、Y）的联合概率密度为。 2、（ ）设是服从标准正态分布的随机变量的分布函数， X是服从正态分布的随机变量，则有3、（ ）设二维随机变量（X、Y）的联合概率密度为，随机变量 的数学期望存在，则4、（ ）设总体X的分布中的未知参数的置信度为的置信区间为 则有。 5、（ ）假设总体X服从区间上的均匀分布，从期望考虑，的矩估计是 （是样本均值）。6、（ ）用MINITAB软件求回归方程，在菜单中选择如下命令即可得： 四、计算题（每小题8分，共87=56分）1、某连锁总店属下有10家分店，每天每家分店订货的概率为p，且每家分店的订货行为是相互独立的，求（1） 每天订货分店的家数X的分布律；（2） 某天至少有一家分店订货的概率。2、现有十个球队要进行乒乓球赛，第一轮是小组循环赛，要把十支球队平分成 两组，上届冠亚军作为种子队分别分在不同的两组，其余八队抽签决定分组， 甲队抽第一支签，乙队抽第二支签。（1）求：甲队抽到与上届冠军队在同一组的概率；（2）求：乙队抽到与上届冠军队在同一组的概率；（3）已知乙队抽到与上届冠军队在同一组，求：甲队也是抽到与上届冠军队在同一组的概率。3、已知随机变量X服从参数为的指数分布，且，求（1）参数； （2）4、设一维随机变量X的分布函数为：，求：（1） X的概率密度；（2） 随机变量Y=2(X+1)的数学期望。5、 设二维随机变量（X，Y）的联合概率密度为 ，求（1）该二维随机变量的联合分布函数值；（2）二维随机变量（X，Y）的函数Z=X+Y的分布函数值FZ(1)。6、 用某种仪器间接测量某物体的硬度，重复测量5次，所得数据是175、173、178、174、176，而用别的精确方法测量出的硬度为179(可看作硬度真值)。设测量硬度服从正态分布，问在水平a =0.05下，用此种仪器测量硬度所得数值是否显著偏低？()7、 某厂生产某种产品使用了3种不同的催化剂（因素A）和4种不同的原料（因素B），各种搭配都做一次试验测得成品压强数据。由样本观察值算出各平方和分别为：SSA=25.17，SSB=69.34，SSE=4.16，SST=98.67，试列出方差分析表，据此检验不同催化剂和不同原料在检验水平a =0.05下对产品压强的影响有没有统计意义？ （）五、综合实验（本题8分，开卷，解答另附于数学实验报告中）072 大学数学一、 填空题（每小题2分，本题共12分）1若事件相互独立，且，则= ；2设随机变量的分布列为：01234560.10.150.20.30.120.10.03则； 3设随机变量服从参数为的Poisson分布，且已知，则； 4设 是来自正态总体的样本，则 ； ；5设是来自总体的一个样本，则 ；6假设某种电池的工作时间服从正态分布，观察五个电池的工作时间（小时），并求得其样本均值和标准差分别为：，若检验这批样本是否取自均值为50（小时）的总体，则零假设为 ，其检验统计量为 。 二、单项选择题（每小题3分，本题共18分）1从数字1，2，3，4，5中，随机抽取3个数字（允许重复）组成一个三位数，其各位数字之和等于9的概率为（ ）A；B；C；D2如果随机变量的密度函数为，则（ ）A0.875； B； C； D3设物件的称重则至少应称多少次？（ ） A16；B15；C4；D204设随机变量X的概率密度函数为，则常数C=（ ） A； B5； C2； D5在一个已通过F检验的一元线性回归方程中，若给定的预测区间精确表示为（ ）A； B；C；D6样本容量为时，样本方差是总体方差的无偏估计量，这是因为（ ） A； B； C； D 三、解下列各题（6小题，共48分）1设总体，为简单随机样本，且证明： （6分）2已知连续型随机变量的分布函数为 试确定常数； 求； 求的密度函数（10分） 3若从10件正品、2件次品的一批产品中，无放回地抽取2次，每次取一个，试求第二次取出次品的概率（6分）4设的密度函数为 求的数学期望和方差； 求与的协方差和相关系数，并讨论与是否相关 （8分）5设二维随机变量在区域上服从均匀分布，其中是由曲线和直线所围成试求的联合分布密度及关于的边缘分布密度 与，并判断是否相互独立（10分）6设随机变量服从区间上的均匀分布，试证明：（为常数）也服从均匀分布（8分）四、应用题：以下是某农作物对三种土壤，两种肥料，每一个处理作四次重复试验后所得产量的方差分析表的部分数据，分别写出各零假设，并完成方差分析表，写出分析结果 （12分）方差来源平方和自由度均方和值临界值土壤因素肥料因素2误差18总和23已知参考临界值： 五. 综合实验报告（10分）请您删除一下内容，O(_)O谢谢！2016年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄Acetylcholine is a neurotransmitter released from nerve endings (terminals) in both the peripheral and the central nervous systems. It is synthesized within the nerve terminal from choline, taken up from the tissue fluid into the nerve ending by a specialized transport mechanism. The enzyme necessary for this synthesis is formed in the nerve cell body and passes down the axon to its end, carried in the axoplasmic flow, the slow movement of intracellular substance (cytoplasm). Acetylcholine is stored in the nerve terminal, sequestered in small vesicles awaiting release. When a nerve action potential reaches and invades the nerve terminal, a shower of acetylcholine vesicles is released into the junction (synapse) between the nerve terminal and the effector cell which the nerve activates. This may be another nerve cell or a muscle or gland cell. Thus electrical signals are converted to chemical signals, allowing messages to be passed between nerve cells or between nerve cells and non-nerve cells. This process is termed chemical neurotransmission and was first demonstrated, for nerves to the heart, by the German pharmacologist Loewi in 1921. Chemical transmission involving acetylcholine is known as cholinergic. Acetylcholine acts as a transmitter between motor nerves and the fibres of skeletal muscle at all neuromuscular junctions. At this type of synapse, the nerve terminal is closely apposed to the cell membrane of a muscle fibre at the so-called motor end plate. On release, acetylcholine acts almost instantly, to cause a sequence of chemical and physical events (starting with depolarization of the motor endplate) which cause contraction of the muscle fibre. This is exactly what is required for voluntary muscles in which a rapid response to a command is required. The action of acetylcholine is terminated rapidly, in around 10 milliseconds; an enzyme (cholinesterase) breaks the transmitter down into choline and an acetate ion. The choline is then available for re-uptake into the nerve terminal. These same principles apply to cholinergic transmission at sites other than neuromuscular junctions, although the structure of the synapses differs. In the autonomic nervous system these include nerve-to-nerve synapses at the relay stations (ganglia) in both the sympathetic and the parasympathetic divisions, and the endings of parasympathetic nerve fibres on non-voluntary (smooth) muscle, the heart, and glandular cells; in response to activation of this nerve supply, smooth muscle contracts (notably in the gut), the frequency of heart beat is slowed, and glands secrete. Acetylcholine is also an important transmitter at many sites in the brain at nerve-to-nerve synapses. To understand how acetylcholine brings about a variety of effects in different cells it is necessary to understand membrane receptors. In post-synaptic membranes (those of the cells on which the nerve fibres terminate) there are many different sorts of receptors and some are receptors for acetylcholine. These are protein molecules that react specifically with acetylcholine in a reversible fashion. It is the complex of receptor combined with acetylcholine which brings about a biophysical reaction, resulting in the response from the receptive cell. Two major types of acetylcholine receptors exist in the membranes of cells. The type in skeletal muscle is known as nicotinic; in glands, smooth muscle, and the heart they are muscarinic; and there are some of each type in the brain. These terms are used because nicotine mimics the action of acetylcholine at nicotinic receptors, whereas muscarine, an alkaloid from the mushroom Amanita muscaria, mimics the action of acetylcholine at the muscarinic receptors. Acetylcholine is the neurotransmitter produced by neurons referred to as cholinergic neurons. In the peripheral nervous system acetylcholine plays a role in skeletal muscle movement, as well as in the regulation of smooth muscle and cardiac muscle. In the central nervous system acetylcholine is believed to be involved in learning, memory, and mood. Acetylcholine is synthesized from choline and acetyl coenzyme A through the action of the enzyme choline acetyltransferase and becomes packaged into membrane-boundvesicles. After the arrival of a nerve signal at the termination of an axon, the vesicles fuse with the cell membrane, causing the release of acetylcholine into thesynaptic cleft. For the nerve signal to continue, acetylcholine must diffuse to another nearby neuron or muscle cell, where it will bind and activate areceptorprotein. There are two main types of cholinergic receptors, nicotinic and muscarinic. Nicotinic receptors are located at synapses between two neurons and at synapses between neurons and skeletal muscle cells. Upon activation a nicotinic receptor acts as a channel for the movement of ions into and out of the neuron, directly resulting indepolarizationof the neuron. Muscarinic receptors, located at the synapses of nerves with smooth or cardiac muscle, trigger a chain of chemical events referred to as signal transduction. For a cholinergic neuron to receive another impulse, acetylcholine must be released from the receptor to which it has bound. This will only happen if the concentration of acetylcholine in the synaptic cleft is very low. Low synaptic concentrations of acetylcholine can be maintained via a hydrolysis reaction catalyzed by the enzyme acetylcholinesterase. This enzyme hydrolyzes acetylcholine into acetic acid and choline. If acetylcholinesterase activity is inhibited, the synaptic concentration of acetylcholine will remain higher than normal. If this inhibition is irreversible, as in the case of exposure to many nerve gases and some pesticides, sweating, bronchial constriction, convulsions, paralysis, and possibly death can occur. Although irreversible inhibition is dangerous, beneficial effects may be derived from transient (reversible) inhibition. Drugs that inhibit acetylcholinesterase in a reversible manner have been shown to improve memory in some people with Alzheimers disease. abstract expressionism, movement of abstract painting that emerged in New York City during the mid-1940s and attained singular prominence in American art in the following decade; also called action painting and the New York school. It was the first important school in American painting to declare its independence from European styles and to influence the development of art abroad. Arshile Gorky first gave impetus to the movement. His paintings, derived at first from the art of Picasso, Mir, and surrealism, became more personally expressive. Jackson Pollocks turbulent yet elegant abstract paintings, which were created by spattering paint on huge canvases placed on the floor, brought abstract expressionism before a hostile public. Willem de Koonings first one-man show in 1948 established him as a highly influential artist. His intensely complicated abstract paintings of the 1940s were followed by images of Woman, grotesque versions of buxom womanhood, which were virtually unparalleled in the sustained savagery of their execution. Painters such as Philip Guston and Franz Kline turned to the abstract late in the 1940s and soon developed strikingly original stylesthe former, lyrical and evocative, the latter, forceful and boldly dramatic. Other important artists involved with the movement included Hans Hofmann, Robert Motherwell, and Mark Rothko; among other major abstract expressionists were such painters as Clyfford Still, Theodoros Stamos, Adolph Gottlieb, Helen Frankenthaler, Lee Krasner, and Esteban Vicente. Abstract expressionism presented a broad range of stylistic diversity within its largely, though not exclusively, nonrepresentational framework. For example, the expressive violence and activity in paintings by de Kooning or Pollock marked the opposite end of the pole from the simple, quiescent images of Mark Rothko. Basic to most abstract expressionist painting were the attention paid to surface qualities, i.e., qualities of brushstroke and texture; the use of huge canvases; the adoption of an approach to space in which all parts of the canvas played an equally vital role in the total work; the harnessing of accidents that occurred during the process of painting; the glorification of the act of painting itself as a means of visual communication; and the attempt to transfer pure emotion directly onto the canvas. The movement had an inestimable influence on the many varieties of work that followed it, especially in the way its proponents used color and materials. Its essential energy transmitted an enduring excitement to the American art scene. Science and technology is quite a broad category, and it covers everything from studying the stars and the planets to studying molecules and viruses. Beginning with the Greeks and Hipparchus, continuing through Ptolemy, Copernicus and Galileo, and today with our work on the International Space Station, man continues to learn more and more about the heavens. From here, we look inward to biochemistry and biology. To truly understand biochemistry, scientists study and see the unseen bystudying the chemistry of biological processes. This science, along with biophysics, aims to bring a better understanding of how bodies work from how we turn food into energy to how nerve impulses transmit.analytic geometry, branch ofgeometryin which points are represented with respect to a coordinate system, such asCartesian coordinates, and in which the approach to geometric problems is primarily algebraic. Its most common application is in the representation of equations involving two or three variables as curves in two or three dimensions or surfaces in three dimensions. For example, the linear equationax+by+c=0 represents a straight line in thexy-plane, and the linear equationax+by+cz+d=0 represents a plane in space, wherea, b, c,anddare constant numbers (coefficients). In this way a geometric problem can be translated into an algebraic problem and the methods of algebra brought to bear on its solution. Conversely, the solution of a problem in algebra, such as finding the roots of an equation or system of equations, can be estimated or sometimes given exactly by geometric means, e.g., plotting curves and surfaces and determining points of intersection. In plane analytic geometry a line is frequently described in terms of its slope, which expresses its inclination to the coordinate axes; technically, the slopemof a straight line is the (trigonometric) tangent of the angle it makes with thex-axis. If the line is parallel to thex-axis, its slope is zero. Two or more lines with equal slopes are parallel to one another. In general, the slope of the line through the points (x1,y1) and (x2,y2) is given bym= (y2-y1) / (x2-x1). The conic sections are treated in analytic geometry as the curves corresponding to the general quadratic equationax2+bxy+cy2+dx+ey+f=0, wherea, b, fare constants anda, b,andcare not all zero. In solid analytic geometry the orientation of a straight line is given not by one slope but by its direction cosines, , , and , the cosines of the angles the line makes with thex-, y-,andz-axes, respectively; these satisfy the relationship 2+2+2= 1. In the same wa