一、(1).期望值=平均值=人數乘以機率 20x0.05+30x0.1+40x0.1+50x0.1+60x0.25+70x0.25+80x0.1+90x0.05=58(人數)
變異數=S^2=(ΣXi-[(ΣXi)^2/n])/n-1=(20^2+30^2+40^2+50^2+60^2+70^2+80^2+90^2-[(20+30+40+50+60+70+80+90)^2/8])/7=(28400-24200)/7=600
(2).E(Y) =15x58=870 V(Y)=15x600=9000
二、二項分配:C20取10x(0.1)^10x(0.9)^10
超幾何分配:C(3600,10)xC(400,10)/C(4000,400)
三、(1.)抽出放回為二項分配，
6顆都紅球機率乘上金額(6/20)^6x30000x6
5顆紅1顆白:(6/20)^5x30000x5+(14/20)^1x10000x1
4顆紅2顆白:(6/20)^4x30000x4+(14/20)^2x10000x2
3顆紅3顆白:(6/20)^3x30000x3+(14/20)^3x10000x3
2顆紅4顆白:(6/20)^2x30000x2+(14/20)^4x10000x4
1顆紅5顆白:(6/20)^1x30000x1+(14/20)^5x10000x5
0顆紅6顆白:(14/20)x10000x6
sum=131.22+364.5+7000+972+9800+2430+10290+5400+9604+9000+8403.5+7058.94=70454.16
(2.)抽出不放回為超幾何分配
6顆都紅球機率乘上金額(6/20)(5/19)(4/18)(3/17)(2/16)(1/15)x30000x6
5顆紅1顆白:(6/20)(5/19)(4/18)(3/17)(2/16)x30000x5+(14/15)x10000x1
4顆紅2顆白:(6/20)(5/19)(4/18)(3/17)x30000x4+(14/16)(13/15)x10000x2
3顆紅3顆白:(6/20)(5/19)(4/18)x30000x3+(14/17)(13/16)(12/15)x10000x3
2顆紅4顆白:(6/20)(5/19)x30000x2+(14/18)(13/17)(12/16)(11/15)x10000x4
1顆紅5顆白:(6/20)x30000x1+(14/19)(13/18)(12/17)(11/16)(10/15)x10000x5
0顆紅6顆白:(14/20)(13/19)(12/18)(11/17)(10/16)(9/15)x10000x6
sum=4.644+58.05+9333.33+371.517+15166.66+1578.95+16058.82+4736.84+13084.97+9000+8608.53+4648.60=70454(與二項分配相等)
四、4勝0敗:(0.4)^4 4勝1敗 (第五場必為勝，前面3勝1敗)
C(4,3)C(4,1)x(0.4)^3(0.6) 4勝2敗 (第六場必為勝，前面3勝2敗)
C(5,3)C(5,2)x(0.4)^3(0.6)^2
五、 600000x3+500000x1=2300000
六、題意不明確
七、(1.) (0.8^2)x0.2=0.128
(2.) 0.8^6x0.8x0.2=0.04194304
