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3 危覿 #
襯覲 X 覿螳 危 覿襯 磯ゼ 蟆曙 X ~ Binomial(n,p)襦 蠍壱覃, 蠏 襯讌(PMF) れ螻 螳.
n: 覯襯企 覦覲牛
p: 螳 炎概 襯(0 < p < 1)
x: n覯 譴 炎概
n: 覯襯企 覦覲牛
p: 螳 炎概 襯(0 < p < 1)
x: n覯 譴 炎概
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9 2覿 蟆 #
> # 100覈 譴 覲 A 讌讌:67覈, 覲 B讌讌:33覈 危蟆讀 Exact binomial test
> binom.test(67, 100, p = 1/2, alternative = "two.sided")
Exact binomial test
data: 67 and 100
number of successes = 67, number of trials = 100, p-value =
0.0008737
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
0.5688272 0.7608015
sample estimates:
probability of success
0.67
>
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10 襯螻 1 #
1. 譯殊襯 覯 覈 1 襯?
> #譯殊 2 讌. size=2 > #1 襯 = 1/6 > dbinom(1:2, size=2, prob=1/6) [1] 0.27777778 0.02777778 >譯殊襯 1 1 襯 0.27777778企, 2 覈 1 襯 0.02777778( 3%)襦 襯 蟆 .
2. A朱 蟇碁 覲給 襯 0.4 , 15覈 覲 蟇碁Π 蟆曙
- 襯覲 X 蠏螻 覿?
- 蠏 = 15 * 0.4 = 6 (蠍磯螳)
- 覿 = 15 * 0.4 * 0.6 = 3.6 (蠏螻 朱 伎 螳? SUM((螳 - 蠏)2) / 螳
- 譴ｸ谿 = SQRT(3.6)
豢 6 螳 蠎讌企朱 蟆 .
<蠏 蟲 るジ 覦覯1: >
襯 企 蠏 豢 6螻 蠏殊る 蟆 .
襯 企 蠏 豢 6螻 蠏殊る 蟆 .
> mean(rbinom(1:10000, size=15, prob=0.4)) [1] 6.0037 > mean(rbinom(1:10000, size=15, prob=0.4)) [1] 5.9804 > mean(rbinom(1:10000, size=15, prob=0.4)) [1] 6.0008 > mean(rbinom(1:10000, size=15, prob=0.4)) [1] 6.0188 > mean(rbinom(1:10000, size=15, prob=0.4)) [1] 5.9974 >
- 5覈 覲給 襯
> #15覈 覲 蟇碁 size=15 > #5覈 覲給 襯 > dbinom(1:5, size=15, prob=0.4) [1] 0.00470185 0.02194197 0.06338790 0.12677580 0.18593784 > max(dbinom(1:5, size=15, prob=0.4)) [1] 0.1859378 >
- 企 10覈 覲給 襯
> 1 - max(pbinom(1:9, size=15, prob=0.4)) [1] 0.0338333 >
- 3覈 8覈 覲給 襯
> bin <- pbinom(1:8, size=15, prob=0.4) > 3覈伎企襦 2蟾讌 觜朱 . > bin[8] - bin[2] [1] 0.8778386 >
3. 4讌ろ 10覓語襯 襦 谿 3螳 危 旧 襷豢 襯?
> pbinom(1:3, size=10, prob=1/4) [1] 0.2440252 0.5255928 0.7758751 >0.7758751. 78% 襯企.
4. 譯殊 3螳襯 讌 襯
> dbinom(1:3, size=3, prob=1/6) [1] 0.34722222 0.06944444 0.00462963 >譯殊 1螳襷 1 襯 0.34722222 願, 2螳襷 1 襯 0.06944444 願, 3螳螳 1 襯 0.00462963企.
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11 襯螻 2 #
5. 豐 10覓語, 5讌ろ(5螳 螳企 1螳襷 ) 谿 9螳襯 襷豢 襯?
> dbinom(1:9, size=10, prob=1/5)[9] [1] 4.096e-06
6. 語 覃伎 る るジ讓曙朱 1 企螻, 結伎 る 殊曙朱 1 企
- 豌 るジ讓 2 蟇磯Μ , 朱 襯
> pbinom(1:10, size=10, prob=1/2) [1] 0.01074219 0.05468750 0.17187500 0.37695313 0.62304687 0.82812500 [7] 0.94531250 0.98925781 0.99902344 1.00000000 > bin <- pbinom(1:10, size=10, prob=1/2) > #るジ讓曙朱 4, 殊曙朱 6 讌企 > bin[6] - bin[5] [1] 0.2050781 > # > bin <- dbinom(1:10, size=10, prob=1/2) > bin [1] 0.0097656250 0.0439453125 0.1171875000 0.2050781250 0.2460937500 [6] 0.2050781250 0.1171875000 0.0439453125 0.0097656250 0.0009765625 > #殊 4 企 襯 るジ讓 6 企 襯襷 蟲覃 . > bin[4] [1] 0.2050781 > bin[6] [1] 0.2050781
- 豌 , 朱 2 企伎 襯
> # 2 企伎 蟆曙 > #殊:5, るジ讓:5 > #殊:4, るジ讓:6 > #殊:6, るジ讓:4 > bin <- dbinom(1:10, size=10, prob=1/2) > sum(bin[4:6]) [1] 0.65625
8. 豐 48レ企. 12譬企, 螳 4レ 讌 企. 1襷れ 4覯 觸 ″() 3 觸 襯
> dbinom(1:3, size=4, prob=4/48)[3] [1] 0.002121914譟磯 襯企. 企 覦 讌 襷手蟲襾..
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