2 1 2 3

4 X~F(x), X {Xi} F(x) 10 Matlab binornd

chi2rnd exprnd frnd f gamrnd

geornd hygernd normrnd

poissrnd trnd t unidrnd unifrnd

1 y=random(name, A1, A2, A3, m, n) name A1, A2, A3 m n 2 y=binornd(n, p, 1,10) n p 1 10 1 U(a,b) 1)unifrnd (a,b) [a,b] a,b] 2)unifrnd (a,b,m, n) m n a b

U a b 1 U(2,8) 10 2 5 (1) y1=unifrnd(2,8) (2) y2=unifrnd(2,8,1,10) (3) y3=unifrnd(2,8,2,5) y1=7.7008 y2=3.3868 5.6411 4.9159 7.3478 6.5726 4.7388 2.1110 6.9284 4.6682 5.6926 y3=[a,b] 6.7516 6.4292 4.4342 7.5014 7.3619 7.5309 3.0576 7.6128 4.4616 2.3473]

2 1)R = normrnd(, ,) 2)R = normrnd(, ,m,n) m n 2 N(10,4) 10 2 5 . (1) y1=normrnd(10,2) (2) y2=normrnd(10,2,1,10) (3) y3=normrnd(10,2,2,5)

3 1) R = exprnd() 2)R = exprnd(,m,n) m n 3 E(0.1) 20 2 6 (1) y1=exprnd(0.1) (2) y2=exprnd(0.1,1,20) (3) y3=exprnd(0.1,2,6) (1) y1=0.0051

(2) y2=[a,b] 0.1465 0.0499 0.0722 0.0115 0.0272 0.0784 0.3990 0.0197 0.0810 0.0485 0.0233] (3) y3=[a,b] 0.1042 0.4619 0.1596 0.0505 0.1615 0.0292 0.0207 0.1974 0.1616 0.1301 0.4182 0.0809] 0.1 1/0.1=10 10 . 10 1 . exprnd(10)

4 1) R = binornd(n, p) 2) R = binornd(n,p,m,n) m n 4 B(10,0.8) 15 3 6 (1) y1=binornd(10,0.8) (2) y2=binornd(10,0.8,1,15) (3) y3=binornd(10,0.8,3,6) 20 X F(x) F-1(x)

F(X)~U(0,1) U~U(0,1), F-1(U) F(x) F(x) U(0,1) Ui,(i=1,2), Xi=F-1 (Ui), Xi ,(i=1,2), F(x) U i Xi 1 X F(x) U(0,1) Ui,(i=1,2), Xi=F(Ui), Xi ,(i=1,2

), F(x) Ui Xi 2 P(X=xi)= pi , i=1, 2, ... F(x) R R~U(0,1) xi X x1 X~F(x) F ( x i 1 ) R F ( x i ), ( i 2, 3,

R F ( x 1 ) 5 X x 0 0 FX ( x ) x 0 x 1 1

x 1 Y min{ X 1 , X 2 , , X n } Y n FY ( y ) 1 1 FX ( y ) 1 1 y 1 Y F ( y ) 1 n

(1 y ) n U ~ U (0,1) RandY 1 (1 U ) n=20 1 10 U=unifrnd(0,1,1,10);

Y=1-(1-U).^(1/20); 1 n 6 1 10000 Randnum=unifrnd(0,2*pi,1,10000); %(0,2pi) xRandnum=cos(Randnum);% yRandnum=sin(Randnum);% plot(xRandnum,yRandnum);

6 1 n m n A f=m/n 2. A . P* p n (1) n 0-1 randnum(n) (2) xrandnum (i)

i 1 0 (3) i 4 ( Matlab .m function binomoni(p,n) pro=zeros(1,n); % randnum = binornd(1,p,1,n);% a=0; for i=1:n a=a+randnum(1,i);% pro(i)=a/i;% end

pro=pro; num=1:n; plot(num,pro,num,p) Matlab binomoni(0.5,1000) Matlab binomoni(0.5,10000) Matlab binomoni(0.3,1000) 1

n 1 X X i n i 1 . mean(x) median(x) x x x

n 1 2 S [a,b] (Xi X ) ] n 1 i 1 2 .

std(x) var(x) range(x) 7 5 100 x=normrnd(0,1,100,5); mean1=mean(x) median1=median(x) std1=std(x) var1=var(x) rang1=range(x) 3.

3 E ( X E ( X )) g1 3 1 n 3 ( X X )

i n i 1 G1 3 s 1 2 s (Xi X ) n 0

g1 >0 g1 <0 g1 0 . y=skewness(x) x x x E ( X E ( X ))4 g2 4 1

4 ( X X ) i G2 n s4 1 2

s ( X X ) i n 3 g2 3

y=kurtosis(x) x x x x 8 5 100 x=normrnd(0,1,100,5); skewness1=skewness(x) kurtosis1=kurtosis(x) 9 5 100 x=exprnd(10,100,5); skewness1=skewness(x) kurtosis1=kurtosis(x)

1 Empirical Cumulative Distribution Function x1 x2 xn n * 1 * 2 x x x

* n 0 k Fn ( x) n 1 * 1 xx

* k x x x x x * k 1 * n 2

1 x1 x2 xn * 1 * 2 x x x * n * *

[ x , x ] 1 n [a,b] a b] m-1 t1 t 2 t m 1 t0=a,tm=b i [a,b] t i 1 , t i ) (i=1 2 [a,b] t , t )

i 1 i m) x i i=1 2 n-1 . 2 [a,b] t i 1 , t i ) i f i i n i v i i j 1

vi g i n 3 fi y i d d [a,b] t i 1 , t i ) y i (i=1,2,,m) gi d

4 (1) data hist(data, k) (2) histfit(data , k) (3) data cdfplot(data) 10 . .

. 100 459 612 926 527 775 402 699 447 621 764

362 452 653 552 859 960 634 654 724 558 624 434 164

513 755 885 555 564 531 378 542 982 487 781 49 610 570

339 512 765 509 640 734 474 697 292 84 280 577 666

584 742 608 388 515 837 416 246 496 763 433 565 428 824

628 473 606 687 468 217 748 706 1153 538 954 677 1062 539

499 715 815 593 593 862 771 358 484 790 544 310 505

680 844 659 609 638 120 581 645 851 x=[459 362 624 542 509 584 433 748 815 505 612 452 434 982 640 742 565 706 593 680 926 653 164 487 734 608 428 1153 593 844 527 552 513 781 474 388 824 538 862 659 775 859 755 49 697 515

628 954 771 609 402 960 885 610 292 837 473 677 358 638 699 634 555 570 84 416 606 1062 484 120 447 654 564 339 280 246 687 539 790 581 621 724 531 512 577 496 468 499 544 645 764 558 378 765 666 763 217 715 310 851] hist(x,10) histfit(x,10) cdfplot(x) 11 10 500

x=exprnd(10,100,1); hist(x,9) cdfplot(x)

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