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Contents

1 覯襯企伎
2 覯襯企 螳
3 危覿
4 危覿
5 襯覦
6
7 覿
8
9 2覿 蟆
10 襯螻 1
11 襯螻 2


1 覯襯企伎 #

  • 炎概 ろ
  • 螻 覓伎螻
  • 覿
  • 覲 螳 觜螳
  • 覃 結
  • 谿 覦

2 覯襯企 螳 #

  • 螳 炎概螻 ろ 螳讌 蟇企 螳讌.
  • 螳 炎概 襯 p, ろ 襯 q = 1 - p襯 螳讌.
  • 螳 襦 襴曙朱 螳 蟆郁骸螳 るジ 蟆郁骸 レ 覩語讌 .

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.
危覿.jpg
n: 覯襯企 覦覲牛
p: 螳 炎概 襯(0 < p < 1)
x: n覯 譴 炎概

4 危覿 #

  • 讌蠍磯ゼ 10覯 蟆曙 覃伎
  • 曙 覲旧 譴 覲 豺
  • 豢 譴 覿
  • 襭襯 20覯 蟆曙 襭炎概

5 襯覦 #

plot(dbinom(0:100, size=100, prob=0.2))
dbinom01.jpg


plot(dbinom(0:100, size=100, prob=0.5))
dbinom02.jpg

6 #

plot(pbinom(0:100, size=100, prob=0.5))
pbinom01.jpg

7 覿 #

plot(qbinom(c(0.2, 0.5, 0.8), size=10, prob=0.5))
qbinom01.jpg

8 #

plot(rbinom(0:100, size=100, prob=0.5))
rbinom01.jpg

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 

> 

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)

<蠏 蟲 るジ 覦覯1: 蠏碁襯 伎 覦覯>
豢 6 螳 蠎讌企朱 蟆 .
problem02.jpg

<蠏 蟲 るジ 覦覯1: >
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
> 
problem01.jpg

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.


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..
蠍 蠍郁鍵..
企: : るジ讓曙 襦螻豺 企Ν 譯殊語. 襦螻豺
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