中北大学概率统计习题册第三章完整标准答案(详解)

第三章随机变量的数字特征班级姓名学号成绩1.设随机变量的分布列为 -1 -2 0 1 2 0.1 0.2 0.4 0.1 0.2试计算：。解：EMBEDEquation.DSMT4EMBEDEquation.DSMT4EMBEDEquation.DSMT42.设随机变量的分布列为：,其中为常数，，。求。解：EMBEDEquation.DSMT4EMBEDEquation.DSMT4所以，3.设随机变量的概率密度 函 关于工期滞后的函关于工程严重滞后的函关于工程进度滞后的回复函关于征求同志党风廉政意见的函关于征求廉洁自律情况的复函 数为，其中为常数，求。解：注：关于绝对收敛性或当时当时综上所述，我们有4.设随机变量表示圆的半径，的概率密度函数为：，求圆的周长和面积的数学期望。解：5．设连续型随机变量的概率密度为：试求数学期望和方差。解：6.设连续型随机变量的概率密度函数为：，且，试求。解：由于是的概率密度，所以有即又得所以所以，从而7.设随机变量的概率密度函数为，且随机变量，求。解：所以的分布律为 Y -1 0 1 0 8.一工厂生产的某种设备的寿命(以年计)的概率密度为工厂规定，出售的设备若在售出一年之内损坏可予以调换。若工厂售出一台设备赢利100元，调换一台设备厂方需花费300元。试求厂方出售一台设备净赢利的数学期望。解：设Y表示出售一台设备的净赢利为Y元，则9.设二维随机变量的联合分布律为试求。解:10.设随机变量与的联合分布律为试证明：与不相关，且不相互独立。并试着写出之间的关系来说明的不相关性。解：由与的联合分布律得 XY -2 -1 1 2 1 0 0.25 0.25 0 0.5 4 0.25 0 0 0.25 0.5 0.25 0.25 0.25 0.25 其中EMBEDEquation.DSMT4，，从而；所以，与不相关；，所以与不相互独立由于显然的分布律与完全相同，所以有，这表明与之间没有线性关系，即它们不相关。11.设随机变量的联合概率密度函数为求：。解：EMBEDEquation.DSMT4EMBEDEquation.DSMT412.设随机变量的联合概率密度为试求。解：13.设某商品每周的需求量服从分布，而经销商店进货量为区间中的某一整数，商店每销售一件商品可获利500元。若供大于求则削价处理，每处理一件商品亏损100元；若供不应求，则可从外部调剂供应，此时每件商品仅获利300元。为使商店所获利润期望值不少于9280元，试确定最少进货量。解：设进货件，则商店获利为由于，其概率密度函数为所以商店所获利润期望值为解此不等式得最少进货量为22件。解法2由于实际中商品件数是整数。本题也可处理成离散型均匀分布，即需求的分布律为，则解此不等式同样得到最少进货量为22件。-14-2013-2014-1_1138643592.unknown_1138719281.unknown_1138773661.unknown_1170769428.unknown_1170769437.unknown_1170770028.unknown_1170770089.unknown_1170770122.unknown_1170770146.unknown_1170770297.unknown_1170770298.unknown_1170770299.unknown_1170770300.unknown_1170770306.unknown_1170770307.unknown_1170770308.unknown_1170770309.unknown_1170770400.unknown_1186425343.unknown_1186425344.unknown_1186425353.unknown_1186425508.unknown_1230037128.unknown_1230037129.unknown_1230037495.unknown_1230037516.unknown_1230037545.unknown_1230037628.unknown_1230037636.unknown_1230037819.unknown_1230037863.unknown_1230037997.unknown_1230039972.unknown_1230040326.unknown_1230040371.unknown_1230040852.unknown_1231070881.unknown_1307359250.unknown_1307359594.unknown_1307359677.unknown_1307441419.unknown_1307441435.unknown_1307441458.unknown_1307477368.unknown_1307477379.unknown_1307477402.unknown_1307477573.unknown_1307477687.unknown_1307477859.unknown_1307541122.unknown_1335544350.unknown_1335544351.unknown_1335546384.unknown_1340119867.unknown_1340119945.unknown_1340120080.unknown_1340120125.unknown_1340120628.unknown_1340120629.unknown_1340120656.unknown_1443424510.unknown_1443424606.unknown_1443424641.unknown_1443424679.unknown_1443424801.unknown_1443424815.unknown_1443424921.unknown_1443424955.unknown_1443425050.unknown_1443425088.unknown_1443425882.unknown_1443425890.unknown_1443425957.unknown_1443425968.unknown_1443426691.unknown_1443426720.unknown_1443426766.unknown_1443426793.unknown_1443426833.unknown_1443426934.unknown_1443426951.unknown_1443427057.unknown_1443427058.unknown_1443427130.unknown_1443427611.unknown_1443427802.unknown_1443427814.unknown_1443430894.unknown_1443430912.unknown_1443430947.unknown_1443431049.unknown_1443431065.unknown_1443431223.unknown_1443431331.unknown_1443431359.unknown_1443431380.unknown_1443431395.unknown_1443431492.unknown_1443431515.unknown_1443431603.unknown_1443432041.unknown_1443432055.unknown_1443432127.unknown_1443432128.unknown_1445542553.unknown_1445542694.unknown_1445542715.unknown_1445542728.unknown_1445542810.unknown_1445542818.unknown_1445542835.unknown_1445542919.unknown_1445542993.unknown_1445543017.unknown_1445543126.unknown_1445543140.unknown_1445543151.unknown_1445543334.unknown_1445543356.unknown_1445543375.unknown_1445543384.unknown_1445543419.unknown_1445543454.unknown_1445543605.unknown_1445543618.unknown_1445543637.unknown_1445543690.unknown_1445543720.unknown_1445544072.unknown_1445544083.unknown_1445544186.unknown_1445544198.unknown_1445544214.unknown_1445544336.unknown_1445544520.unknown_1445544530.unknown_1445544615.unknown_1445544775.unknown_1445544822.unknown_1445545860.unknown_1445545871.unknown_1445545930.unknown_1445546026.unknown_1445546097.unknown_1445546105.unknown_1445546177.unknown_1445546254.unknown_1445546326.unknown_1445546343.unknown_1445546363.unknown_1445546471.unknown_1445546472.unknown_1445546588.unknown_1445546696.unknown_1445546728.unknown_1445546859.unknown_1445546871.unknown_1445546878.unknown_1445546890.unknown_1445546944.unknown_1445547000.unknown_1445547020.unknown_1445547080.unknown_1445547148.unknown_1445547162.unknown_1445547193.unknown_1445547368.unknown_1445547547.unknown_1445547644.unknown_1445547657.unknown_1445547684.unknown_1445547693.unknown_1445547756.unknown_1445548032.unknown_1445548039.unknown_1445548078.unknown_1445548106.unknown_1445548119.unknown_1445548128.unknown_1445548319.unknown_1445548429.unknown_1445548440.unknown_1445548451.unknown_1445548552.unknown_1445548779.unknown_1445548789.unknown_1445548897.unknown_1445548980.unknown_1445549218.unknown_1445549336.unknown_1445549371.unknown_1445549595.unknown_1445549706.unknown_1445549707.unknown_1445550062.unknown_1445550063.unknown_1445551706.unknown_1445551965.unknown_1445553186.unknown_1445553328.unknown_1445553336.unknown_1445553692.unknown