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第二章 随机变量及其分布 PowerPoint PPT Presentation


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第二章 随机变量及其分布. 关键词: 随机变量 概率分布函数 离散型随机变量 连续型随机变量 随机变量的函数. 常见的两类试验结果:. §1 随机变量. 示数的 —— 降雨量; 候车人数; 发生交通事故的次数 …. 示性的 —— 明天天气(晴,云 … ); 化验结果(阳性,阴性) …. s. x. e. 中心问题:将试验结果数量化. X=f(e) --为 S 上的单值函数, X 为实数.

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第二章 随机变量及其分布

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1


s

x

e

X=f(e)SX



2

()



X

c.



3p0<p<1XX


Ai={i}P(Ai)=pi=1,2,3 A1,A2,A3


3

2

1

X

0

p

p(1-p)

p

(1-p)2p

(1-p)3


X

0

1

q

p

p

01

X

01

(p+q=1,p>0,q>0)

Xp0-1.



S01


01


,A,P(A)=p,(0<p<1).A, p0-1:

Bernoulli


  • nE ,p(A)=p,0<p<1,Enn


  • n:

  • nA={1}


52nA={}


AnX

Xp


Ai={ iA }n=3


,10255p.


A={} XY2.

Xb(10,p)Yb(5,p){X=i}{Y=j}



X

(Poisson)

X


(1)13

(2)543


200110003


X

X


ababN,nXX


X

Xp


  • p0<p<1XXp


X

X(r,p).


  • p0<p<1,rXX(r,p)


  • pSXX(S,p)


3


X

1

0

p

p

q

p>0,q>0,q+p=1.


1

q

0

1


  • A,BA,B3A,B1/4A,BAX X


4

:X

X



  • X

    (1)c

    (2)X

    (3) k



X

15Y(1)Y;(2)Y


X

X(a,b)XU(a,b)


1(-1,2)XX

210100


1 X(-1,2)

210Y0


>0X

X


X


X (Gauss)

X




()

()


  • X

  • X




aX

1a0.005

2a0.0085


()

(1)=100=297.8cm

(2)=10090%(97,103)


X 2540033350


X

Y

5

X

Y=g(X)Y


1

0

-1

X

pi

0.2

0.5

0.3

X

Y=X2Y


Y0,1

(Y=0)(X=0)

(Y=1)(X=1)(X=-1)


X

Y=


X,Y


Y(0,16)


XY=g(X)Y


0

1

-1

X

Y=2X,Z=X2,Y,Z


2

Y

-2

0

1

0

Z

p

p

Y-2,0,2

Z0,1

(Y=-2)(X=-1)

(Z=1)(X=1)(X=-1)



X~U(-1, 2)


X~N(0, 1)


y

y=g(x)

y

h(y),y

0

x




!


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