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ホーエル 『 初等統計学 』 第5章 主要な確率分布 PowerPoint PPT Presentation


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青山学院大学社会情報学部 「統計入門」第7・8回. ホーエル 『 初等統計学 』 第5章 主要な確率分布. 寺尾 敦 青山学院大学社会情報学部 atsushi [at] si.aoyama.ac.jp Twitter: @ aterao. この章で学ぶこと. 代表的な2つの確率分布の導入 2項分布(離散型) 正規分布(連続型) 2項分布の正規近似. クイズ.

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ホーエル 『 初等統計学 』 第5章 主要な確率分布

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atsushi [at] si.aoyama.ac.jp

Twitter: @aterao


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  • 150100


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1.

  • trialBernoulli trial


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  • binominal distribution p nindependent X. B(n, p)

    • X


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p.94

  • p.95

  • XX

  • xP{X = x}


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X

FFF

0

FFS

SFF

1

FSF

FSS

2

SFS

3

SSF

SSS


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    • X

    • X

  • n


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n=3

  • FSS

  • FFS


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  • 0


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  • n x

  • nx


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  • binominal coefficient


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  • p.97 p.100

    • binom_2010.pdf

    • IIIII

    • 1011


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  • p.97 p.100

  • binom_2010.pdf

Course Power


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2.


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  • np npq

    • q1 p


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  • p X1

  • P{X1=1}= p, P{X1=0} = q


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  • n X


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  • 150100


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  • 1/2

    • coefficient of variation


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1, 0.707, 0.707

0.5, 0.5, 1

1.5, 0.866, 0.577


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3.

  • p.86

    • bell curve

  • normal distribution


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  • probability density function


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  • 2N(, 2)


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X=a X=b


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X


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a

b

X


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  • =168%

    • X

  • 2 =195%

  • 3 =199.7%


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  • standard normal distribution

  • Z P{0Zz} p.295IVP{zZ}


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  • 2 XX Z

    • 0 .

    • 1/2 1/


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  • raw scorestandardized score

  • 1050


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4.

  • n

    • normal approximation


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  • p= q = 1/2

    • npnpq

  • p = 1/2p qn

    • np> 5p1/2nq > 5


P 1 3 n 12

p=1/3, n=12

np > 5


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    • np npq

  • 01


10 p 1 3 n 24

10p=1/3, n=24 ()


10 p 1 3 n 241

10p=1/3, n=24


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  • xXZ

  • 0 |z|

    • |z|

    • z = 0 x x = 0 x = np


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    • z > 0 z < 0

    • z 0 z0.5

    • z 0 z0.5


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    • 4.5

    • p.109p.110


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