n=7，n=8和n=9的二項(xiàng)式表
二項(xiàng)式隨機(jī)變量提供了離散隨機(jī)變量的一個重要例子。二項(xiàng)式分布描述了我們隨機(jī)變量的每個值的概率，可以通過兩個參數(shù)完全確定：n和p。這里n是獨(dú)立試驗(yàn)的次數(shù)，p是每次試驗(yàn)的恒定成功概率。下表提供了n=7,8和9的二項(xiàng)式概率。每個概率四舍五入到小數(shù)點(diǎn)后三位。
應(yīng)該使用二項(xiàng)式分布嗎？。在跳入使用此表之前，我們需要檢查是否滿足以下條件：
- 我們有有限數(shù)量的觀察或試驗(yàn)。
- 每個試驗(yàn)的結(jié)果可以分為成功或失敗。
- 成功的概率保持不變。
- 觀察結(jié)果彼此獨(dú)立。
當(dāng)滿足這四個條件時，二項(xiàng)分布將在總共n個獨(dú)立試驗(yàn)的實(shí)驗(yàn)中給出r成功的概率，每個試驗(yàn)的成功概率p。表中的概率通過公式C（n，r）pr（1-p）n-r其中C（n，r）是組合的公式。每個值都有單獨(dú)的表格n.表中的每個條目由p和r的值組織。
其他表格
對于其他二項(xiàng)分布表，我們有n=2到6，n=10到11。當(dāng)n p和n（1-p）的值均大于或等于10時，我們可以使用二項(xiàng)式分布的正態(tài)近似。這給了我們一個很好的概率近似值，不需要計算二項(xiàng)式系數(shù)。這提供了一個很好的結(jié)果優(yōu)點(diǎn)，因?yàn)檫@些二項(xiàng)式計算可能非常復(fù)雜。
示例
遺傳學(xué)與概率有很多聯(lián)系。我們將看一個來說明二項(xiàng)式分布的使用。假設(shè)我們知道后代遺傳兩個隱性基因拷貝（因此具有我們正在研究的隱性特征）的概率是1/4。
此外，我們想計算一個八人家庭中一定數(shù)量的孩子具有這種特征的概率。設(shè)X是具有這種特征的孩子的數(shù)量。我們看一下表格中的n=8和p=0.25的列，請參閱下文：
.100
.267.311.208.087.023.004
這就意味著我們的例子
- P（X=0）=10.0%，這是沒有一個孩子具有隱性特征的概率。
- P（X=1）=26.7%，這是其中一個孩子具有隱性特征的概率。
- P（X=2）=31.1%，這是兩個孩子具有隱性特征的概率。
- P（X=3）=20.8%，這是三個孩子具有隱性特征的概率。
- P（X=4）=8.7%，這是四個孩子具有隱性特征的概率。
- P（X=5）=2.3%，這是五個孩子具有隱性特征的概率。
- P（X=6）=0.4%，這是其中六個孩子具有隱性特征的可能性。
n=7至n=9
的表141 n 142 7
| p | .01 | .05 | .10 | .15 | .20 | .25 | .30 | .35 | .40 | .45 | .50 | .55 | .60 | .65 | .70 | .75 | .80 | .85 | .90 | .95 | |
| 0 | .932 | .698 | .478 | .321 | .210 | .133 | .082 | .049 | .028 | .015 | .008 | .004 | .002 | .001 | .000 | .000 | .000 | .000 | .000 | .000 | |
| 1 | .066 | .257 | .372 | .396 | .367 | .311 | .247 | .185 | .131 | .087 | .055 | .032 | .017 | .008 | .004 | .001 | .000 | .000 | .000 | .000 | |
| 2 | .002 | .041 | .124 | .210 | .275 | .311 | .318 | .299 | .261 | .214 | .164 | .117 | .077 | .047 | .025 | .012 | .004 | .001 | .000 | .000 | |
| 3 | .000 | .004 | .023 | .062 | .115 | .173 | .227 | .268 | .290 | .292 | .273 | .239 | .194 | .144 | .097 | .058 | .029 | .011 | .003 | .000 | |
| 4 | .000 | .000 | .003 | .011 | .029 | .058 | .097 | .144 | .194 | .239 | .273 | .292 | .290 | ;268 | .227 | .173 | .115 | .062 | .023 | .004 | |
| 5 | .000 | .000 | .000 | .001 | .004 | .012 | .025 | .047 | .077 | .117 | .164 | .214 | .261 | .299 | .318 | .311 | .275 | .210 | .124 | .041 | |
| 6 | .000 | .000 | .000 | .000 | .000 | .001 | .004 | .008 | .017 | .032 | .055 | .087 | .131 | .185 | .247 | .311 | .367 | .396 | .372 | .257 | |
| 7 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .001 | .002 | .004 | .008 | .015 | .028 | .049 | .082 | .133 | .210 | .321 | .478 | .698 |
675>n=8
| p | .01 | .05 | .10 | .15 | .20 | .25 | .30 | .35 | .40 | .45 | .50 | .55 | .60 | .65 | .70 | .75 | .80 | .85 | .90 | .95 | |
| r | 0 | .923 | .663 | .430 | .272 | .168 | .100 | .058 | .032 | .017 | .008 | .004 | .002 | .001 | .000 | .000 | .000 | .000 | .000 | .000 | .000 |
| 1 | .075 | .279 | .383 | .385 | .336 | .267 | .198 | .137 | .090 | .055 | .031 | .016 | .008 | .003 | .001 | .000 | .000 | .000 | .000 | .000 | |
| 2 | .003 | .051 | .149 | .238 | .294 | .311 | .296 | .259 | .209 | .157 | .109 | .070 | .041 | .022 | .010 | .004 | .001 | .000 | .000 | .000 | |
| 3 | .000 | .005 | .033 | .084 | .147 | .208 | .254 | .279 | .279 | .257 | .219 | .172 | .124 | .081 | .047 | .023 | .009 | .003 | .000 | .000 | |
| 4 | .000 | .000 | .005 | :018 | .046 | .087 | .136 | .188 | .232 | .263 | .273 | .263 | .232 | .188 | .136 | .087 | .046 | .018 | .005 | .000 | |
| 5 | .000 | .000 | .000 | .003 | .009 | .023 | .047 | .081 | .124 | .172 | .219 | .257 | .279 | .279 | .254 | .208 | .147 | .084 | .033 | .005 | |
| 6 | .000 | .000 | .000 | .000 | .001 | .004 | .010 | .022 | .041 | .070 | .109 | .157 | .209 | .259 | .296 | .311 | .294 | .238 | .149 | .051 | |
| 7 | .000 | .000 | .000 | .000 | .000 | .000 | .001 | .003 | .008 | .016 | .031 | .055 | .090 | .137 | .198 | .267 | .336 | .385 | .383 | .279 | |
| 8 | .000 | .000 | .000 | .000 | .000 | 000 | .000 | .000 | .001 | .002 | .004 | .008 | .017 | .032 | .058 | .100 | .168 | .272 | .430 | .663 |
1258>n=9
| r | 1317>p.01 | .05 | 1329>.10.15 | .20 | .25 | .30 | .35 | .40 | .45 | .50 | .55 | .60 | .65 | .70 | .75 | .80 | .85 | .90 | .95 | 0 | .914 | .630 | .387 | .232 | .134 | .075 | .040 | .021 | .010 | .005 | .002 | .001 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 |
| 1453>1 | .083 | .299 | .387 | .368 | .302 | .225 | .156 | .100 | .060 | .034 | .018 | .008 | .004 | .001 | .000 | .000 | .000 | .000 | .000 | .000 | |
| 2 | .003 | .063 | .172 | .260 | .302 | .300 | .267 | .216 | .161 | .111 | .070 | .041 | .021 | .010 | .004 | .001 | .000 | .000 | .000 | .000 | |
| 3 | .000 | .008 | .045 | .107 | .176 | .234 | .267 | .272 | .251 | .212 | .164 | .116 | .074 | .042 | .021 | .009 | .003 | .001 | .000 | .000 | |
| 4 | .000 | .001 | .007 | .028 | .066 | .117 | .172 | .219 | .251 | .260 | .246 | .213 | .167 | .118 | .074 | .039 | .017 | .005 | .001 | .000 | |
| 5 | .000 | .000 | .001 | .005 | .017 | .039 | .074 | .118 | .167 | .213 | .246 | .260 | .251 | .219 | .172 | .117 | .066 | .028 | .007 | .001 | |
| 6 | .000 | .000 | .000 | .001 | .003 | .009 | .021 | .042 | .074 | .116 | .164 | .212 | .251 | .272 | .267 | .234 | .176 | .107 | .045 | .008 | |
| 7 | .000 | .000 | .000 | .000 | .000 | .001 | .004 | .010 | .021 | 結(jié)核病的防治健康知識.041 | .070 | .111 | .161 | .216 | .267 | .300 | .302 | .260 | .172 | .063 | 1785年|
| 8 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .001 | .004 | .008 | .018 | .034 | .060 | .100 | .156 | .225 | .302 | .368 | .387 | .299 | |
| 9 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .000 | .001 | .002 | .005 | .010 | .021 | .040 | .075 | .134 | .232 | .387 | .630 | 1881年1882年1883年 1886年
