probability theory basic jp
TRANSCRIPT
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I
1
http://www.slideshare.net/ShinjiNakaoka
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2
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3
() A
(i)(ii)(iii)
P.1-2
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4
B A
P.2-3
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Bayes
5
()
1 ()
2
A
P.4-5
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6
()
A, B
A, B
Ai
P.5-6
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A
A
n k (combination)
n k : (permutation)
P.6-13
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8
X
X (probability mass function)
X
x FX()=1
P.17-18
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9
X ()
(stieltjes )
Xn n
P.19-22
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10
X
P.19-22
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11
X
X ()
( etc)
( Laplace )
P.19-22
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12
(hypergeometric) n1 n-n1 () r k
n1 =80 n-n1 =20 50 k 40
P.23-27
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13
(Bernoulli) n1 n-n1 () p=n1/n X=1 ()X=0 () ()
p =0.2 1 Bernoulli 10000 0 8000 1 2000
P.23-27
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14 P.23-27
(binomial) p Bernoulli n k
p =0.2 1 Bernoulli 10000
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(geometric) p X X
p =0.2 10000 20 4,5
P.23-27
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(negative binomial) p r X X
p =0.2 3 10000 ()
P.23-27
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Poisson
17
Poisson Poisson
()
P.23-27
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X, Y (joint distribution)
X (marginal distribution)
X, Y
P.34-35
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19 P.34-35
X, Y
X, Y
X (marginal)
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20 P.34-35
X, Y
X, Y
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X X
Y=y
P.34-35
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()
22
(Covariance)
(correlation coefficient)
P.35-36
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X B
fX(x) fX(x)
dx (x,x+dx]
X
P.28-33
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X ()
()
X
()
P.28-33
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25
(exponential) X
X X
=1
ATM
P.28-33
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26
(normal / Gauss) X
X X ()
=1, =1 ) ()
P.28-33
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27
(Gamma) X
X Gamma Gamma
=1, k=3 ) mRNA
P.28-33
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28
(uniform) X
X
b=1, a=0 )
X
P.28-33