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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


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s

x

e

X=f(e)SX


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2

()


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X

c.


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3p0<p<1XX


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


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3

2

1

X

0

p

p(1-p)

p

(1-p)2p

(1-p)3


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X

0

1

q

p

p

01

X

01

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

Xp0-1.


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S01


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01


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

Bernoulli


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  • nE ,p(A)=p,0<p<1,Enn


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  • n:

  • nA={1}


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52nA={}


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AnX

Xp


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Ai={ iA }n=3


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664p0<p<1

1

2.


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,10255p.


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A={} XY2.

XB(10,p)YB(5,p){X=i}{Y=j}


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X

(Poisson)

X


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(1)13

(2)543


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200110003


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X

X


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ababN,nXX


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X

Xp


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  • p0<p<1XXp


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X

X(r,p).


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  • p0<p<1,rXX(r,p)


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3


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X

1

0

p

p

q

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


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1

q

0

1


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  • A,BA,B3A,B1/4A,BAX X


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4

:X

X


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  • X

    (1)c

    (2)X

    (3) k


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X

15Y(1)Y;(2)Y


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X

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


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1(-1,2)XX

210100


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1 X(-1,2)

210Y0


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6306:20XX050

115

21510


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6:30 6:50

1P(15)=25/50=0.5

(2) P(10)=30/50=3/5

P(1510)=21/23/5=3/5

6:20 6:30 6:45 7:00 7:10


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>0X

X


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X


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X (Gauss)

X


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()

()


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  • X

  • X


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1 0.005

2 0.0085


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()

(1)=100=297.8cm

(2)=10090%(97,103)


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X 2540033350


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X

Y

5

X

Y=g(X)Y


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1

0

-1

X

pi

0.2

0.5

0.3

X

Y=X2Y


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Y0,1

(Y=0)(X=0)

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


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X


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X,Y


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Y(0,16)


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XY=g(X)Y


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0

1

-1

X

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


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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)


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X~U(-1, 2)


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X~N(0, 1)


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y

y=g(x)

y

h(y),y

0

x


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!


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