I

1

http://www.slideshare.net/ShinjiNakaoka

2

3

() A

(i)(ii)(iii)

P.1-2

4

B A

P.2-3

Bayes

5

()

1 ()

2

A

P.4-5

6

()

A, B

A, B

Ai

P.5-6

7

A

A

n k (combination)

n k : (permutation)

P.6-13

8

X

X (probability mass function)

X

x FX()=1

P.17-18

9

X ()

(stieltjes )

Xn n

P.19-22

10

X

P.19-22

11

X

X ()

( etc)

( Laplace )

P.19-22

12

(hypergeometric) n1 n-n1 () r k

n1 =80 n-n1 =20 50 k 40

P.23-27

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

14 P.23-27

(binomial) p Bernoulli n k

p =0.2 1 Bernoulli 10000

15

(geometric) p X X

p =0.2 10000 20 4,5

P.23-27

16

(negative binomial) p r X X

p =0.2 3 10000 ()

P.23-27

Poisson

17

Poisson Poisson

()

P.23-27

18

X, Y (joint distribution)

X (marginal distribution)

X, Y

P.34-35

19 P.34-35

X, Y

X, Y

X (marginal)

20 P.34-35

X, Y

X, Y

21

X X

Y=y

P.34-35

()

22

(Covariance)

(correlation coefficient)

P.35-36

23

X B

fX(x) fX(x)

dx (x,x+dx]

X

P.28-33

24

X ()

()

X

()

P.28-33

25

(exponential) X

X X

=1

ATM

P.28-33

26

(normal / Gauss) X

X X ()

=1, =1 ) ()

P.28-33

27

(Gamma) X

X Gamma Gamma

=1, k=3 ) mRNA

P.28-33

28

(uniform) X

X

b=1, a=0 )

X

P.28-33