2016年广播电视大学应用概率统计复习试题资料.doc

学生姓名：学号：专业年级：成绩：一、 填空题（每小题2分，本题共16分）1、设随机变量，则。 （ 已知标准正态分布函数值：）2、设随机变量服从泊松分布且具有方差2，那么的分布律为 。3、设一维连续型随机变量的概率密度函数为，则随机变量的概率密度函数为 。4、以下是利用minitab对变量和的线性相关性作回归分析所得结果，由此判定回归 方程是 。the regression equation isy = 0.63 + 0.040 xanalysis of variancesource df ss ms f pregression 1 0.178 0.178 0.13 0.725residual error 9 12.200 1.356total 10 12.3785、设总体是它的一个样本，则 服从 分布。6、设正态总体的均方差，该总体的一个容量为的样本的样本均值，则 总体均值的置信水平为95%的置信区间是 。7、在双因素有交互作用的方差分析中，设因素有3个水平，因素有2个水平，每个 处理作两次重复试验，则试验误差平方和的自由度 。8、设关于的线性回归方程为，则。 （ ）二、单项选择题（每小题2分，本题共18分）1、设则。 2、设是相互独立的两个随机变量，则。3、二维随机变量的分布函数。 4、多个相互独立的服从正态分布的随机变量的线性组合服从。二项分布 泊松分布 均匀分布 正态分布 5、以下哪一个minitab命令用于作回归分析。 6、以下哪一个matlab命令用于求定积分。 7、设总体，对检验水平，欲检验方差由容量为的一个样本计算出来的统计量的观察值应与作比较。 8、参数的点估计量的无偏性指的是。 9、设是总体的一个样本，则总体方差的矩法估计量是。 三、计算题（每小题8分，本题共56分）1、在次品率为5%的一批产品中任取5件，求其中至少有两件次品的概率。2、以下是某农作物对三种土壤，四种肥料，每一个处理作三次重复试验后所得产量的方差分析表的部分数据，完成方差分析表并写出分析结果。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误差总和（参考临界值：）3、某工厂生产的一种电子设备的寿命（以1000小时为单位）服从以为参数的指数分布。设产品的单位成本是200元，售价是500元。但是，如果，则工厂承担全部退款。试求工厂承担全部退款的概率以及一件产品的期望利润。4、某工厂生产的某种产品的合格率为92%，假定质检系统是经过简化的，对合格品以96%的概率给出合格的结果，对不合格品同样以96%的概率给出不合格的结果。试求产品经质检后为合格品的概率，又问一件经检验为合格品的产品确是合格品的概率是多少？ 5、假定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）为： 32，41，42，49，53问这批样本是否取自均值为50（小时）的总体？（） （）6、设二维随机变量的联合概率密度函数如下，试求，并问与是否相互独立？7、已知随机变量的概率密度函数为，求的分布函数 及事件的概率。四、综合实验（本题10分，开卷，解答另附于数学实验报告中）华南农业大学期末考试试卷（a卷）2003学年 第二学期考试科目：应用概率统计（答案）评卷人：学生姓名：学号：专业年级：成绩：一、 填空题（每小题2分，本题共16分）1、设随机变量，则。 （ 已知标准正态分布函数值：）2、设随机变量服从泊松分布且具有方差2，那么的分布律为。3、设一维连续型随机变量的概率密度函数为，则随机变量的概率密度函数为 。4、以下是利用minitab对变量和的线性相关性作回归分析所得结果，由此判定回归 方程是 无效的 。the regression equation isy = 0.63 + 0.040 xanalysis of variancesource df ss ms f pregression 1 0.178 0.178 0.13 0.725residual error 9 12.200 1.356total 10 12.3785、设总体是它的一个样本，则 服从分布。6、设正态总体的均方差，该总体的一个容量为的样本的样本均值，则 总体均值的置信水平为95%的置信区间是或 。7、在双因素有交互作用的方差分析中，设因素有3个水平，因素有2个水平，每个 处理重复两次试验，则试验误差平方和的自由度 6 。8、设关于的线性回归方程为，则。 （ ）二、单项选择题（每小题2分，本题共18分）1、设则。 2、设是相互独立的两个随机变量，则。3、二维随机变量的分布函数。 4、多个相互独立的服从正态分布的随机变量的线性组合服从。二项分布 泊松分布 均匀分布 正态分布 5、以下哪一个minitab命令用于作回归分析。 6、以下哪一个matlab命令用于求定积分。 7、设总体，对检验水平，欲检验方差由容量为的一个样本计算出来的统计量的观察值应与作比较。 8、参数的点估计量的无偏性指的是。 9、设是总体的一个样本，则总体方差的矩法估计量是。 三、计算题（每小题8分，本题共56分）1、在次品率为5%的一批产品中任取5件，求其中至少有两件次品的概率。解：设表示5件产品中次品的数目，则 （2分）所求的概率为 （3分） （2分） （1分）2、以下是某农作物对三种土壤，四种肥料，每一个处理作三次重复试验后所得产量的方差分析表的部分数据，完成方差分析表并写出分析结果。方差来源平方和自由度均方和值临界值土壤因素214.360.28肥料因素3186.993.71614.780.29误差2450.44总和35（参考临界值： ）（表格：5分）分析结果：因为， 所以因素，即肥料对农作物产量的影响是有统计意义的，而因素，即土壤对农作物的产量的影响没有统计意义，肥料和土壤之间也不存在交互效应。 （3分）3、某工厂生产的一种电子设备的寿命（以1000小时为单位）服从以为参数的指数分布。设产品的单位成本是200元，售价是500元。但是，如果，则工厂承担全部退款。试求工厂要承担全部退款的概率及一件产品的期望利润。解： （4分） 令表示一件产品的利润，则的分布律为：（分布律：2分）一件产品的期望利润（元） （4分）4、某工厂生产的某种产品的合格率为92%，假定质检系统是经过简化的，对合格品以96%的概率给出合格的结果，对不合格品同样以96%的概率给出不合格的结果。试求产品经质检后为合格品的概率，又问一件经检验为合格品的产品确是合格品的概率是多少？解：设a 表示任取的一件产品是合格品，b表示任取的一件产品被检验为合格品。 则产品经质检后为合格品的概率： （4分） 一件经检验为合格品的产品确是合格品的概率为： （4分）5、假定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）为： 32，41，42，49，53问这批样本是否取自均值为50（小时）的总体？（） （）解法一：已知 检验假设： （2分）因为总体方差未知，所以用t统计量作检验： （2分）由样本计算得的观察值为： （2分）所以接受假设，可以认为这批样本是取自均值为50（小时）的总体。 （2分）解法二：已知 检验假设： （2分）因为总体方差未知，所以用t统计量作检验： （2分）由样本计算得的观察值为： （2分）所以接受假设，可以认为这批样本是取自均值为50（小时）的总体。 （2分）6、设二维随机变量的联合概率密度函数如下，试求，并问与是否相互独立？解：（1） （2分） （2） （2分） （2分）显然, ;所以，x 与 y 非相互独立。 （2分）7、已知随机变量的概率密度函数为，求的分布函数 及事件的概率。解：（1）当时， 当时， 当时， 综上所述， （4分） （2） （2分） （2分）四、综合实验（本题10分，开卷，解答另附于数学实验报告中）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basketball can make a true claim to being the only major sport that is an american invention. from high school to the professional level, basketball attracts a large following for live games as well as television coverage of events like the national collegiate athletic association (ncaa) annual tournament and the national basketball association (nba) and womens national basketball association (wnba) playoffs. and it has also made american heroes out of its player and coach legends like michael jordan, larry bird, earvin magic johnson, sheryl swoopes, and other great players. at the heart of the game is the playing space and the equipment. the space is a rectangular, indoor court. the principal pieces of equipment are the two elevated baskets, one at each end (in the long direction) of the court, and the basketball itself. the ball is spherical in shape and is inflated. basket-balls range in size from 28.5-30 in (72-76 cm) in circumference, and in weight from 18-22 oz (510-624 g). for players below the high school level, a smaller ball is used, but the ball in mens games measures 29.5-30 in (75-76 cm) in circumference, and a womens ball is 28.5-29 in (72-74 cm) in circumference. the covering of the ball is leather, rubber, composition, or synthetic, although leather covers only are dictated by rules for college play, unless the teams agree otherwise. orange is the regulation color. at all levels of play, the home team provides the ball. inflation of the ball is based on the height of the balls bounce. inside the covering or casing, a rubber bladder holds air. the ball must be inflated to a pressure sufficient to make it rebound to a height (measured to the top of the ball) of 49-54 in (1.2-1.4 m) when it is dropped on a solid wooden floor from a starting height of 6 ft (1.80 m) measured from the bottom of the ball. the factory must test the balls, and the air pressure that makes the ball legal in keeping with the bounce test is stamped on the ball. during the intensity of high school and college tourneys and the professional playoffs, this inflated sphere commands considerable attention. basketball is one of few sports with a known date of birth. on december 1, 1891, in springfield, massachusetts, james naismith hung two half-bushel peach baskets at the opposite ends of a gymnasium and out-lined 13 rules based on five principles to his students at the international training school of the young mens christian association (ymca), which later became springfield college. naismith (1861-1939) was a physical education teacher who was seeking a team sport with limited physical contact but a lot of running, jumping, shooting, and the hand-eye coordination required in handling a ball. the peach baskets he hung as goals gave the sport the name of basketball. his students were excited about the game, and christmas vacation gave them the chance to tell their friends and people at their local ymcas about the game. the association leaders wrote to naismith asking for copies of the rules, and they were published in the triangle, the school newspaper, on january 15,1892. naismiths five basic principles center on the ball, which was described as large, light, and handled with the hands. players could not move the ball by running alone, and none of the players was restricted against handling the ball. the playing area was also open to all players, but there was to be no physical contact between players; the ball was the objective. to score, the ball had to be shot through a horizontal, elevated goal. the team with the most points at the end of an allotted time period wins. early in the history of basketball, the local ymcas provided the gymnasiums, and membership in the organization grew rapidly. the size of the local gym dictated the number of players; smaller gyms used five players on a side, and the larger gyms allowed seven to nine. the team size became generally established as five in 1895, and, in 1897, this was made formal in the rules. the ymca lost interest in supporting the game because 10-20 basketball players monopolized a gymnasium previously used by many more in a variety of activities. ymca membership dropped, and basketball enthusiasts played in local halls. this led to the building of basketball gymnasiums at schools and colleges and also to the formation of professional leagues. although basketball was born in the united states, five of naismiths original players were canadians, and the game spread to canada immediately. it was played in france by 1893; england in 1894; australia, china, and india between 1895 and 1900; and japan in 1900. from 1891 through 1893, a soccer ball was used to play basketball. the first basketball was manufactured in 1894. it was 32 in (81 cm) in circumference, or about 4 in (10 cm) larger than a soccer ball. the dedicated basketball was made of laced leather and weighed less than 20 oz (567 g). the first molded ball that eliminated the need for laces was introduced in 1948; its construction and size of 30 in (76 cm) were ruled official in 1949. the rule-setters came from several groups early in the 1900s. colleges and universities established their rules committees in 1905, the ymca and the amateur athletic union (aau) created a set of rules jointly, state militia groups abided by a shared set of rules, and there were two professional sets of rules. a joint rules committee for colleges, the aau, and the ymca was created in 1915, and, under the name the national basketball committee (nbc) made rules for amateur play until 1979. in that year, the national federation of state high school associations began governing the sport at the high school level, and the ncaa rules committee assumed rule-making responsibilities for junior colleges, colleges, and the armed forces, with a similar committee holding jurisdiction over womens basketball. until world war ii, basketball became increasingly popular in the united states especially at the high school and college levels. after world war ii, its popularity grew around the world. in the 1980s, interest in the game truly exploded because of television exposure. broadcast of the ncaa championship games began in 1963, and, by the 1980s, cable television was carrying regular season college games and even high school championships in some states. players like bill russell, wilt chamberlain, and lew alcindor (kareem abdul-jabbar) became nationally famous at the college level and carried their fans along in their professional basketball careers. the womens game changed radically in 1971 when separate rules for women were modified to more closely resemble the mens game. television interest followed the women as well with broadcast of ncaa championship tourneys beginning in the early 1980s and the formation of the wnba in 1997. internationally, italy has probably become the leading basketball nation outside of the united states, with national, corporate, and professional teams. the olympics boosts basketball internationally and has also spurred the womens game by recognizing it as an olympic event in 1976. again, television coverage of the olympics has been exceptionally important in drawing attention to international teams. the first professional mens basketball league in the united states was the national basketball league (nbl), which debuted in 1898. players were paid on a per-game basis, and this league and others were hurt by the poor quality of games and the ever-changing players on a team. after the great depression, a new nbl was organized in 1937, and the basketball association of america was organized in 1946. the two leagues came to agree that players had to be assigned to teams on a contract basis and that high standards had to govern the game; under these premises, the two joined to form the national basketball association (nba) in 1949. a rival american basketball association (aba) was inaugurated in 1967 and challenged the nba for college talent and market share for almost ten years. in 1976, this league disbanded, but four of its teams remained as nba teams. unification came just in time for major television support. several womens professional leagues were attempted and failed, including the womens professional basketball league (wbl) and the womens world basketball association, before the wnba debuted in 1997 with the support of the nba. james naismith, originally from al-monte, ontario, invented basketball at the international ymca training school in springfield, massachusetts, in 1891. the game was first played with peach baskets (hence the name) and a soccer ball and was intended to provide indoor exercise for football players. as a result, it was originally a rough sport. although ten of naismiths original thirteen rules remain, the game soon changed considerably, and the founder had little to do with its evolution. the first intercollegiate game was played in minnesota in 1895, with nine players to a side and a final score of nine to three. a year later, the first five-man teams played at the university of chicago. baskets were now constructed of twine nets but it was not until 1906 that the bottom of the nets were open. in 1897, the dribble was first used, field goals became two points, foul shots one point, and the first professional game was played. a year later, the first professional league was started, in the east, while in 1900, the first intercollegiate league began. in 1910, in order to limit rough play, it was agreed that four fouls would disqualify players, and glass backboards were used for the first time. nonetheless, many rules still differed, depending upon where the games were played and whether professionals, collegians, or ymca players were involved. college basketball was played from texas to wisconsin and throughout the east through the 1920s, but most teams played only in their own regions, which prevented a national game or audience from developing. professional basketball was played almost exclusively in the east before the 1920s, except when a team would barnstorm into the midwest to play local teams, often after a league had folded. before the 1930s very few games, either professional or amateur, were played in facilities suitable for basketball or with a perfectly round ball. some were played in arenas with chicken wire separating the players from fans, thus the word cagers, others with posts in the middle of the floor and often with balconies overhanging the corners, limiting the areas from which shots could be taken. until the late 1930s, all players used the two-hand set shot, and scores remained low. basketball in the 1920s and 1930s became both more organized and more popular, although it still lagged far behind both baseball and college football. in the pros, five urban, ethnic teams excelled and played with almost no college graduates. they were the new york original celtics; the cleveland rosenblums, owned by max rosenblum; eddie gottliebs philadelphia sphas (south philadelphia hebrew association); and two great black teams, the new york renaissance five and abe sapersteins harlem globetrotters, which was actually from chicago. while these teams had some notable players, no superstars, such as babe ruth, jack dempsey, or red grange, emerged to capture the publics attention as they did in other sports of the period. the same was true in college basketball up until the late 1930s, with coaches dominating the game and its development. walter doc meanwell at wisconsin, forrest phog allen at kansas, ward piggy lambert at purdue, and henry doc carlson at pittsburgh all made significant contributions to the games development: zone defenses, the weave, the passing game, and the fast break. in the decade preceding world war ii, five events changed college basketball and allowed it to become a major spectator sport. in 1929, the rules committee reversed a decision that would have outlawed dribbling and slowed the game considerably. five years later, promoter edward ned irish staged the first intersectional twin bill in madison square garden in new york city and attracted more than 16,000 fans. he demonstrated the appeal of major college ball and made new york its center. in december 1936, hank luisetti of stanford revealed the virtues of the one-handed shot to an amazed garden audience and became the first major collegiate star. soon thereafter, luisetti scored an incredible fifty points against duquesne, thus ending the easts devotion to the set shot and encouraging a more open game. in consecutive years the center jump was eliminated after free throws and then after field goals, thus speeding up the game and allowing for more scoring. in 1938, irish created the national invitation tournament (nit) in the garden to determine a national champion. although postseason tournaments had occurred before, the nit was the first with major colleges from different regions and proved to be a great financial success. the national collegiate athletic association (ncaa) created its own postseason tournament in 1939 but did not rival the nit in prestige for some time. the 1940s sa