Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Теория вероятностей и математическая статистика на базе Maple. Лабораторный практикум. Учебное пособие
.pdf
x
ɛ ɫ ɜ ɏ ɢɦɟɟɬ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɧɚ ɨɬɪɟɡɤɟ
xfx
>@
ɇɚɣɞɢɬɟ ɬɚɤɨɟ ɨɩɬɢɦɚɥɶɧɨɟ ɦɟɫɬɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɝɚɪɚɠɚ ɱɬɨɛɵ ɨɠɢ
ɞɚɟɦɨɟ ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɦɟɫɬɚ ɩɨɥɨɦɤɢ ɝɪɭɡɨɜɢɤɨɜ ɞɨ ɝɚɪɚɠɚ
ɛɵɥɨɦɢɧɢɦɚɥɶɧɨ
Ⱦɪɭɝɢɦɢɫɥɨɜɚɦɢɧɚɣɞɢɬɟ ɬɚɤɨɟ ɪɚɫɫɬɨɹɧɢɟ bɦɟɠɞɭ
ɝɚɪɚɠɨɦ ɢ ɩɭɧɤɬɨɦ Ⱥ ɩɪɢ ɤɨɬɨɪɨɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɫɥɭɱɚɣɧɨɣ
ɜɟɥɢɱɢɧɵ_X±b_ɛɵɥɨɛɵɦɢɧɢɦɚɥɶɧɵɦ
f
DzȇȈȕȗȇșȕȗȔȇȦȗȇȈȕșȇ
ǻǺǴDZǽǯǯǸDzǺǾǧǰǴȂǼǩǬDzǯǾǯǴ
ǻȚȔȑȝȏȏȕȋȔȕȊȕȘȒȚȞȇȐȔȕȊȕȇȗȊȚȓȌȔșȇ
ɉɭɫɬɶ ɏ ± ɞɢɫɤɪɟɬɧɚɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ Y MXȼɷɬɨɦɫɥɭɱɚɟɞɥɹ
ɨɬɵɫɤɚɧɢɹɜɟɪɨɹɬɧɨɫɬɟɣɜɨɡɦɨɠɧɵɯɡɧɚɱɟɧɢɣɫɜYɫɥɟɞɭɟɬɫɥɨɠɢɬɶɜɟɪɨɹɬɧɨ
ɫɬɢɬɟɯɜɨɡɦɨɠɧɵɯɡɧɚɱɟɧɢɣɫɜɏɩɪɢɤɨɬɨɪɵɯɫɜYɩɪɢɧɢɦɚɟɬɨɞɢɧɚɤɨɜɵɟ
ɡɧɚɱɟɧɢɹ
ǹǬǵǷǬdzǧɉɭɫɬɶɏ±ɧɟɩɪɟɪɵɜɧɚɹɫɥɭɱɚɣɧɚɹɜɟɥɢɱɢɧɚ ɫɩɥɨɬɧɨɫɬɶɸ
ɪɚɫɩɪɟɞɟɥɟɧɢɹfxM±ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɚɹɫɬɪɨɝɨɦɨɧɨɬɨɧɧɚɹɮɭɧɤɰɢɹɧɚɩɪɨ
ɦɟɠɭɬɤɟɌɜɫɟɯɡɧɚɱɟɧɢɣɫɜɏɌɨɝɞɚɩɥɨɬɧɨɫɬɶgyɪɚɫɩɪɟɞɟɥɟɧɢɹɫɥɭɱɚɣɧɨɣ
ɜɟɥɢɱɢɧɵY MXɟɫɬɶɮɭɧɤɰɢɹ
ɡɧɚɱɟɧɢɣɫɜY.
MM ɧɚɩɪɨɦɟɠɭɬɤɟMTɜɫɟɯ
__
yy
c
ȿɫɥɢ ɠɟ ɮɭɧɤɰɢɹ M ɧɟ ɫɬɪɨɝɨ ɦɨɧɨɬɨɧɧɚ ɧɚ ɩɪɨɦɟɠɭɬɤɟ Ɍɜɫɟɯɡɧɚɱɟ
ɧɢɣɫɜɏɬɨɫɥɟɞɭɟɬɪɚɡɛɢɬɶɌɧɚɬɚɤɢɟkɩɪɨɦɟɠɭɬɤɨɜɧɚɤɨɬɨɪɵɯɮɭɧɤɰɢɹM
ɫɬɪɨɝɨ ɦɨɧɨɬɨɧɧɚ ɢ ɧɚɣɬɢ ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ g
y ɞɥɹ ɤɚɠɞɨɝɨ
i
ɢɡ ɩɪɨɦɟɠɭɬɤɨɜ ɦɨɧɨɬɨɧɧɨɫɬɢ ɚ ɡɚɬɟɦ ɩɪɟɞɫɬɚɜɢɬɶ gy ɜ ɜɢɞɟ ɫɭɦɦɵ
gy g y
¦
i
i
ǸDzǬǫǸǹǩǯǬ ɉɭɫɬɶ ɫ ɜ ɏ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɚ ɧɚ ɢɧɬɟɪɜɚɥɟ
Fy ± ɧɟɤɨɬɨɪɚɹ ɧɟɭɛɵɜɚɸɳɚɹ ɮɭɧɤɰɢɹ ɫ ɦɧɨɠɟɫɬɜɨɦ ɡɧɚɱɟɧɢɣ
> @ ɩɪɢɱɟɦ Fy ɫɬɪɨɝɨ ɜɨɡɪɚɫɬɚɟɬ ɤɨɝɞɚ Fy Ɍɨɝɞɚ Fy ɹɜɥɹɟɬɫɹ
ɧɚɤɨɩɢɬɟɥɶɧɨɣɮɭɧɤɰɢɟɣɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵY F
ȾɟɣɫɬɜɢɬɟɥɶɧɨɮɭɧɤɰɢɹMx F
±
xɨɩɪɟɞɟɥɟɧɚɢɦɨɧɨɬɨɧɧɨ ɜɨɡɪɚɫɬɚɟɬ
±
X
ɧɚɦɧɨɠɟɫɬɜɟɜɫɟɯɡɧɚɱɟɧɢɣɫɜɏɄɪɨɦɟɬɨɝɨɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɩɪɢ
x
ɫɜɏɪɚɜɧɚ
fx
®
ɩɪɢ
¯
x
ɩɪɟɞɟɥɟɧɢɹgyɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵY MX F
ɉɨɷɬɨɦɭɜɫɢɥɭɬɟɨɪɟɦɵɩɥɨɬɧɨɫɬɶɪɚɫ
±
Xɪɚɜɧɚ
c
ɟɫɥɢ
Fy Fy
MM
__
fy yfFyFy
cc
®
ɟɫɥɢ ɢɥɢ
¯
Fy Fy
ɬɟgy Fcy ɉɨɫɥɟɞɧɟɟɢɨɡɧɚɱɚɟɬɱɬɨFyɹɜɥɹɟɬɫɹɧɚɤɨɩɢɬɟɥɶɧɨɣɮɭɧɤ
ɰɢɟɣɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵYȽɪɚɮɢɤɮɭɧɤɰɢɹFyɨɤɨɬɨɪɨɣɝɨɜɨɪɢɬɫɹɜɫɥɟɞ
ɫɬɜɢɟɦɨɠɟɬɜɵɝɥɹɞɟɬɶɧɚɩɪɢɦɟɪɬɚɤɪɢɫ
ǷȏȘ
ɋɥɟɞɫɬɜɢɟ ɩɨɡɜɨɥɹɟɬ ɦɨɞɟɥɢɪɨɜɚɬɶ ɫɥɭɱɚɣɧɭɸ ɜɟɥɢɱɢɧɭ Yɫɩɪɟɞɩɢ
ɫɚɧɧɨɣɧɚɤɨɩɢɬɟɥɶɧɨɣɮɭɧɤɰɢɟɣFyɩɪɢɩɟɪɟɱɢɫɥɟɧɧɵɯɜɵɲɟɨɝɪɚɧɢɱɟɧɢɹɯ
ɧɚ Fy ɞɥɹ ɷɬɨɝɨ ɞɨɫɬɚɬɨɱɧɨ ɝɟɧɟɪɢɪɨɜɚɬɶ ɪɚɜɧɨɦɟɪɧɨ ɱɢɫɥɚ ɯ ɧɚ ɢɧɬɟɪɜɚ
ɥɟɢɡɚɬɟɦɜɵɱɢɫɥɹɬɶɡɧɚɱɟɧɢɹy F
±
x
Ɉɞɧɚɤɨɧɟ ɜɫɟɝɞɚ 0DSOH ɜ ɫɨɫɬɨɹɧɢɢɧɚɣɬɢ ɫɢɦɜɨɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɮɭɧɤ
±
ɰɢɢF
x
ɤɨɪɟɧɶy
xȼɷɬɨɦɫɥɭɱɚɟɞɥɹɤɚɠɞɨɝɨiɝɨɪɚɜɧɨɦɟɪɧɨɫɝɟɧɟɪɢɪɨɜɚɧɧɨɝɨɱɢɫɥɚ
ɢɡ ɢɧɬɟɪɜɚɥɚ ɫɥɟɞɭɟɬɱɢɫɥɟɧɧɨ ɪɟɲɢɬɶ ɭɪɚɜɧɟɧɢɟ xi Fy ɨɩɪɟɞɟɥɢɜ
i
ɉɨɥɭɱɟɧɧɚɹɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɱɢɫɟɥyy«yi«ɢɛɭɞɟɬɜɵɛɨɪ
i
ɤɨɣɫɜYɢɦɟɸɳɟɣɡɚɞɚɧɧɭɸɧɚɤɨɩɢɬɟɥɶɧɭɸɮɭɧɤɰɢɸFy
ǮȇȋȇȔȏȌ 1ǫȏȘȑȗȌșȔȇȦȘȉǼȎȇȋȇȔȇȗȦȋȕȓȗȇȘȖȗȌȋȌȒȌȔȏȦ
Ǽ î î
p
ɇɚɣɞɢɬɟɪɹɞɪɚɫɩɪɟɞɟɥɟɧɢɹɫɜY=X.
ǮȇȋȇȔȏȌ 2
ɇɟɩɪɟɪɵɜɧɚɹɫɜɏɢɦɟɟɬɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹɤɨɬɨɪɚɹɪɚɜɧɚfx
ɩɪɢx >ab@ɢɪɚɜɧɚ±ɜɨɫɬɚɥɶɧɵɯɫɥɭɱɚɹɯɇɚɣɬɢɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹ
gyɫɜY ±X ɢɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹhyɫɜY X
ɇɟɩɪɟɪɵɜɧɚɹɫɜɏɢɦɟɟɬɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹɤɨɬɨɪɚɹɪɚɜɧɚfx
ɩɪɢ x>a b@ ɢ ɪɚɜɧɚ ± ɜ ɨɫɬɚɥɶɧɵɯ ɫɥɭɱɚɹɯ ɇɚɣɬɢ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟ
ɧɢɹgyɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵY ±X
ɇɟɩɪɟɪɵɜɧɚɹ ɫ ɜ ɏ ɢɦɟɟɬ ɩɨɤɚɡɚɬɟɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫ ɩɚɪɚɦɟɬ
ɪɨɦ a ɝɞɟ a ! ɇɚɣɬɢ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ gy ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ
Y ±X
ɇɟɩɪɟɪɵɜɧɚɹɫɜɏɪɚɜɧɨɦɟɪɧɨɪɚɫɩɪɟɞɟɥɟɧɚɧɚɨɬɪɟɡɤɟ>@ɇɚɣɬɢ
ɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹgyɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵY ±X
ɇɟɩɪɟɪɵɜɧɚɹɫɜɏɢɦɟɟɬɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹfxɇɚɣɬɢɩɥɨɬ
ɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹgyɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵY MX _X_
s
f
f
ǮȇȋȇȔȏȌ 3ǵșȗȕȐșȌțȇȐȒɎɭɧɤɰɢɢɋɥȼɟɥPZVɢɜɚɦɫɬɚɧɟɬɞɨɫɬɭɩɧɚɩɪɨɰɟɞɭ
ɪɚ
DensFunc(f,s) ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɹɟɬ ɧɚɯɨɞɢɬɶ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
gyɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵY MXɝɞɟM±ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɚɹɮɭɧɤɰɢɹɧɚɩɪɨ
ɦɟɠɭɬɤɟ Ɍ ɜɫɟɯ ɡɧɚɱɟɧɢɣ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɏ ɫ ɡɚɞɚɧɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫ
ɩɪɟɞɟɥɟɧɢɹ
fȾɥɹɜɵɩɨɥɧɟɧɢɹɩɪɨɰɟɞɭɪɵDensFuncɧɟɨɛɯɨɞɢɦɨɚɪɚɡɛɢɬɶɌ
ɧɚɬɚɤɢɟkɩɪɨɦɟɠɭɬɤɨɜɧɚɤɨɬɨɪɵɯɮɭɧɤɰɢɹMɫɬɪɨɝɨɦɨɧɨɬɨɧɧɚɛɧɚɤɚɠɞɨɦ
y
M
ɢɡɷɬɢɯkɩɪɨɦɟɠɭɬɤɨɜɧɚɣɬɢɮɭɧɤɰɢɸ
ɫɨɤ
sɪɚɜɧɵɣ
> @
yy y
M M M
k
i «kɜ ɫɨɫɬɚɜɢɬɶ ɫɩɢ
i
ȼɧɚɱɚɥɟɩɪɢɜɟɞɟɦɨɛɪɚɡɰɵ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯ ɤɨɦɚɧɞ ɩɚɤɟɬɚ 0DSOHɤɨ
ɬɨɪɵɟɩɨɧɚɞɨɛɹɬɫɹɩɪɢɜɵɩɨɥɧɟɧɢɹɷɬɨɝɨɡɚɞɚɧɢɹ
Ɂɚɞɚɧɢɟɤɭɫɨɱɧɨɧɟɩɪɟɪɵɜɧɨɣɮɭɧɤɰɢɢɫɩɨɦɨɳɶɸɤɨɦɚɧɞɵ
piecewise
f:=piecewise(x<-3,x^2,x>=-3 and x<5,sin(x),x>=5,exp(2*x));
xx
°
VLQ DQG
xxx
d
®
°
x
H
¯
x
x
tdt
ȼɵɱɢɫɥɟɧɢɟɨɩɪɟɞɟɥɟɧɧɨɝɨɢɧɬɟɝɪɚɥɚ
³
f
ɫɩɨɦɨɳɶɸɤɨɦɚɧɞɵint
f:=piecewise(t<=0,0,0<t and t<=Pi/2,cos(t),0);
°
°
FRV WDQG
ft t
d
®
°
°
¯
t
d
otherwise
S
F:=int(f,t=-infinity..x);
x
x
x
x
x
°
°
°
Fxx
VLQ
d
®
°
°
°
¯
x
d
S
S
ɍɩɪɨɳɟɧɢɟɪɟɡɭɥɶɬɚɬɚɜɵɱɢɫɥɟɧɢɹɫɩɨɦɨɳɶɸɤɨɦɚɧɞɵ
simplify
h:=(x^2+2*x+1)/(x^2-3*x-4);
h
x
x
simplify(%);
xx
ɉɪɟɜɪɚɳɟɧɢɟ ɜɵɪɚɠɟɧɢɹ ɡɚɜɢɫɹɳɟɝɨ ɨɬ ɯ ɜ ɮɭɧɤɰɢɸ ɫ ɚɪɝɭɦɟɧɬɨɦ ɯ
ɫɩɨɦɨɳɶɸɤɨɦɚɧɞɵ
unapply
h:=(x+1)/(x-4);
xx
h
h:=unapply(h,x);
x
hx
o
x
h(1);
ȼ ɡɚɞɚɱɚɯ ± ɞɚɧɚ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ fx ɫɥɭɱɚɣɧɨɣ ɜɟɥɢ
M
f
P
ɱɢɧɵɏ
ɇɚɣɞɢɬɟ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɧɚɤɨɩɢɬɟɥɶɧɭɸ ɮɭɧɤɰɢɸ
ɫɜY
XɚɬɚɤɠɟɜɟɪɨɹɬɧɨɫɬɶɫɨɛɵɬɢɹPa Y b
ɋɜɏ ɪɚɫɩɪɟɞɟɥɟɧɚ ɪɚɜɧɨɦɟɪɧɨ ɧɚ ɢɧɬɟɪɜɚɥɟ S Y FRVX
a ±b
ɋɜɏɢɦɟɟɬɫɬɚɧɞɚɪɬɧɨɟɪɚɫɩɪɟɞɟɥɟɧɢɟY Xa b
ɋɜɏɢɦɟɟɬɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɥɟSY X
ǮȇȋȇȔȏȌ 4ǸȉǼȏȓȌȌșȔȕȗȓȇȒȣȔȕȌȗȇȘȖȗȌȋȌȒȌȔȏȌȘȖȇȗȇȓȌșȗȇȓȏPȏVY aX b
b S
aS
VLQ
xx ɧɚ ɢɧɬɟɪɜɚ
ɋɩɨɦɨɳɶɸɩɪɨɰɟɞɭɪɵ
ɧɨɟɪɚɫɩɪɟɞɟɥɟɧɢɟɫɩɚɪɚɦɟɬɪɚɦɢa
DensFuncɞɨɤɚɡɚɬɶɱɬɨɫɜYɢɦɟɟɬɧɨɪɦɚɥɶ
bɢ_a_V
ǮȇȋȇȔȏȌ 5
ɂɡɦɟɪɹɟɬɫɹ ɞɥɢɧɚ ɪɟɛɪɚ ɤɭɛɚ Ɋɟɡɭɥɶɬɚɬɵ ɢɡɦɟɪɟɧɢɣ ɦɨɠɧɨ ɪɚɫɫɦɚɬ
ɪɢɜɚɬɶɤɚɤɫɜɏɪɚɜɧɨɦɟɪɧɨɪɚɫɩɪɟɞɟɥɟɧɧɭɸɧɚɢɧɬɟɪɜɚɥɟ
ɋ ɩɨɦɨɳɶɸ ɩɪɨɰɟɞɭɪɵ
DensFunc ɧɚɣɞɢɬɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ
ɢ ɫɪɟɞɧɟɟ ɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɜɵɪɚɠɚ
ɸɳɟɣɢɡɦɟɪɟɧɧɭɸɜɟɥɢɱɢɧɭɨɛɴɟɦɚɤɭɛɚ
Ɏɢɥɢɩɩɫɬɨɢɬɧɚ ɛɟɪɟɝɭ ɪɟɤɢɢɜɵɛɢɪɚɟɬɫɥɭɱɚɣɧɵɦ ɨɛɪɚɡɨɦ ɧɚɩɪɚɜ
x
ɥɟɧɢɟ ɞɜɢɠɟɧɢɹ ɜ ɤɨɬɨɪɨɦ ɨɧ ɦɨɝ ɭɞɚɥɢɬɶɫɹ ɨɬ ɪɟɤɢ Ɏɢɥɢɩɩ ɩɪɟɞɩɨɥɚɝɚɟɬ
ɩɪɨɣɬɢɚ ɤɦɩɨɩɪɹɦɨɣɜɜɵɛɪɚɧɧɨɦɧɚɩɪɚɜɥɟɧɢɢ
ɇɚɣɬɢɨɠɢɞɚɟɦɨɟɪɚɫɫɬɨɹɧɢɟɎɢɥɢɩɩɚɨɬɪɟɤɢɧɚɤɨɬɨɪɨɦɨɧɨɤɚɠɟɬ
ɫɹɩɪɨɣɞɹɚ ɤɦ
S
Y X
ɋɜɏɢɦɟɟɬɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹ fx FRVx ɧɚɢɧɬɟɪɜɚɥɟ
ɋɩɨɦɨɳɶɸɩɪɨɰɟɞɭɪɵ
DensFuncɧɚɣɞɢɬɟɞɢɫɩɟɪɫɢɸɫɥɭɱɚɣɧɨɣɜɟɥɢ
ɱɢɧɵY
ǮȇȋȇȔȏȌ 6 ǩȔȇȞȇȒȌȖȗȏȉȌȋȌȓ ȕȈȗȇȎȝȢ ȉȢȖȕȒȔȌȔȏȦșȌȜ ȑȕȓȇȔȋ0DSOHȑȕșȕȗȢȌ Ȗȕ
ȔȇȋȕȈȦșȘȦȖȗȏȉȢȖȕȒȔȌȔȏȏȤșȕȊȕȎȇȋȇȔȏȦ
±
ɇɚɯɨɠɞɟɧɢɟ ɫɢɦɜɨɥɶɧɨɝɨ ɜɵɪɚɠɟɧɢɹ ɮɭɧɤɰɢɢ y F
ɮɭɧɤɰɢɢx Fyɫɩɨɦɨɳɶɸɜɫɬɪɨɟɧɧɨɣɩɪɨɰɟɞɭɪɵ
solve
x ɨɛɪɚɬɧɨɣ ɞɥɹ
F:=1-exp(-a*y);
ObF
±ay
OQ x
a
F ±H
ObF:=solve(x=F,y);
F:=7*y^2-y+3;
F y
±y
ObF:=solve(x=F,y);
ObF
x
Ⱦɥɹɢɡɜɥɟɱɟɧɢɹɷɥɟɦɟɧɬɚɢɥɢɷɥɟɦɟɧɬɨɜɢɡɦɧɨɠɟɫɬɜɚɢɥɢɫɩɢɫɤɚɪɚɧɟɟ
f
ɭɠɟɢɫɩɨɥɶɡɨɜɚɥɚɫɶɤɨɦɚɧɞɚ
opɗɬɭɤɨɦɚɧɞɭɦɨɠɧɨɩɪɢɦɟɧɹɬɶɞɥɹɢɡɜɥɟɱɟɧɢɹ
ɥɸɛɵɯɜɥɨɠɟɧɧɵɯɨɛɴɟɤɬɨɜɇɚɩɪɢɦɟɪ
f:=piecewise(t<=0,0,0<t and t<=Pi/2,cos(t),0);
°
°
ft t
FRV WDQG
d
®
°
°
¯
t
d
otherwise
S
op(%)[4];
FRVt
Ɉɬɪɨɣɬɟɮɚɣɥ
elRandVal_1
ɉɪɨɰɟɞɭɪɚ
ɆɨɞɟɥɋɥȼɟɥPZVɢɜɚɦɫɬɚɧɭɬɞɨɫɬɭɩɧɵɩɪɨɰɟɞɭɪɵMod-
ɢ ModelRandVal_2
ModelRandVal_1(FOb,n,nb,yy) ɩɨɡɜɨɥɹɟɬɦɨɞɟɥɢɪɨɜɚɬɶ
ɫɥɭɱɚɣɧɭɸ ɜɟɥɢɱɢɧɭ Y ɫ ɩɪɟɞɩɢɫɚɧɧɨɣ ɧɚɤɨɩɢɬɟɥɶɧɨɣ ɮɭɧɤɰɢɟɣ Fy ɜ ɬɨɦ
ɫɥɭɱɚɟɤɨɝɞɚ 0DSOH ɜɫɨɫɬɨɹɧɢɢɧɚɣɬɢɫɢɦɜɨɥɶɧɨɟɜɵɪɚɠɟɧɢɟɨɛɪɚɬɧɨɣɮɭɧɤ
±
ɰɢɢF
ɦɟɬɪ
FOb ɉɚɪɚɦɟɬɪ n ɡɚɞɚɟɬ ɱɢɫɥɨɝɟɧɟɪɢɪɭɟɦɵɯ ɡɧɚɱɟɧɢɣɫ ɜ Yɩɚɪɚ
nb ɡɚɞɚɟɬ ɱɢɫɥɨ ɩɪɹɦɨɭɝɨɥɶɧɢɤɨɜ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ ɩɚɪɚɦɟɬɪ yyɡɚɞɚɟɬ
ɞɢɚɩɚɡɨɧ ɧɚ ɤɨɬɨɪɨɦ ɫɬɪɨɹɬɫɹ ɝɢɫɬɨɝɪɚɦɦɚ ɝɟɧɟɪɢɪɭɟɦɵɯ ɡɧɚɱɟɧɢɣɫɜY
ɢɝɪɚɮɢɤɩɥɨɬɧɨɫɬɢfy
ȼɡɚɞɚɱɚɯ± ɡɚɞɚɧɚ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ fyɫɜY&ɩɨɦɨɳɶɸ
ɜɵɩɨɥɧɢɬɟɫɥɟɞɭɸɳɢɟɞɟɣɫɬɜɢɹ
0DSOH
ɚɧɚɣɞɢɬɟɧɚɤɨɩɢɬɟɥɶɧɭɸɮɭɧɤɰɢɸFyɫɜY
ɛɜɵɞɟɥɢɬɟɬɭ©ɱɚɫɬɶªF
yɮɭɧɤɰɢɢFyɜɤɨɬɨɪɨɣFyɫɬɪɨɝɨɜɨɡɪɚɫɬɚ
ɟɬɨɬɞɨ
Fy
ɜɧɚɣɞɢɬɟɫɢɦɜɨɥɶɧɨɟɜɵɪɚɠɟɧɢɟɮɭɧɤɰɢɢ
ɝ ɫ ɩɨɦɨɳɶɸ ɩɪɨɰɟɞɭɪɵ
ModelRandVal_1 ɩɨɫɬɪɨɣɬɟ ɝɢɫɬɨɝɪɚɦɦɭ n
ɡɧɚɱɟɧɢɣɫɜYɢɝɪɚɮɢɤɩɥɨɬɧɨɫɬɢfy
VLQ
yy ɜɢɧɬɟɪɜɚɥɟSɚɜɧɟɷɬɨɝɨɢɧɬɟɪɜɚɥɚfy
ǮȇȋȇȔȏȌ 7
y
fy e
ɜɢɧɬɟɪɜɚɥɟfɚɜɧɟɷɬɨɝɨɢɧɬɟɪɜɚɥɚfy
ɉɪɨɰɟɞɭɪɚ
ɥɹɟɬ ɦɨɞɟɥɢɪɨɜɚɬɶ ɫ ɜ Y ɫ ɩɪɟɞɩɢɫɚɧɧɨɣ ɧɚɤɨɩɢɬɟɥɶɧɨɣ ɮɭɧɤɰɢɟɣ
ModelRandVal_2proc(F,n,nb,ymin,ymax,yy) ɩɨɡɜɨ
F Fy
ɜɬɨɦɫɥɭɱɚɟɤɨɝɞɚ0DSOHɧɟɜɫɨɫɬɨɹɧɢɢɧɚɣɬɢɫɢɦɜɨɥɶɧɨɟɜɵɪɚɠɟɧɢɟɨɛɪɚɬ
±
ɧɨɣ ɮɭɧɤɰɢɢ F
ɩɚɪɚɦɟɬɪ
nbɡɚɞɚɟɬɱɢɫɥɨɩɪɹɦɨɭɝɨɥɶɧɢɤɨɜɧɚ ɝɢɫɬɨɝɪɚɦɦɟɩɚɪɚɦɟɬɪyyɡɚɞɚ
x ɉɚɪɚɦɟɬɪ n ɡɚɞɚɟɬ ɱɢɫɥɨ ɝɟɧɟɪɢɪɭɟɦɵɯ ɡɧɚɱɟɧɢɣ ɫ ɜ Y
ɟɬ ɞɢɚɩɚɡɨɧ ɧɚ ɤɨɬɨɪɨɦ ɫɬɪɨɹɬɫɹ ɝɢɫɬɨɝɪɚɦɦɚ ɝɟɧɟɪɢɪɭɟɦɵɯ ɡɧɚɱɟɧɢɣ ɫ ɜ Y
ɢɝɪɚɮɢɤ ɩɥɨɬɧɨɫɬɢfy
ymin;ymax)± ɢɧɬɟɪɜɚɥɫɬɪɨɝɨɣ ɦɨɬɨɪɧɨɫɬɢɮɭɧɤ
ɰɢɹFy
ȼɡɚɞɚɱɚɯ± ɡɚɞɚɧɚ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ fy ɫ ɜ Y & ɩɨɦɨɳɶɸ
ɜɵɩɨɥɧɢɬɟɫɥɟɞɭɸɳɢɟɞɟɣɫɬɜɢɹ
0DSOH
ɚɧɚɣɞɢɬɟɧɚɤɨɩɢɬɟɥɶɧɭɸɮɭɧɤɰɢɸFyɫɜY
ɛɜɵɞɟɥɢɬɟɬɭ©ɱɚɫɬɶªF
yɮɭɧɤɰɢɢFyɜɤɨɬɨɪɨɣFyɫɬɪɨɝɨɜɨɡɪɚɫɬɚ
ɟɬɨɬɞɨ
ɜ ɫ ɩɨɦɨɳɶɸ ɩɪɨɰɟɞɭɪɵ
ModelRandVal_2 ɩɨɫɬɪɨɣɬɟ ɝɢɫɬɨɝɪɚɦɦɭ n
ɡɧɚɱɟɧɢɣɫɜYɢɝɪɚɮɢɤɩɥɨɬɧɨɫɬɢfy
fy y ɜɢɧɬɟɪɜɚɥɟɚɜɧɟɷɬɨɝɨɢɧɬɟɪɜɚɥɚfy
fy y ɜɢɧɬɟɪɜɚɥɟɚɜɧɟɷɬɨɝɨɢɧɬɟɪɜɚɥɚfy
ǸȚȓȓȢȘȒȚȞȇȐȔȢȜȉȌȒȏȞȏȔ
ɉɭɫɬɶXɢY±ɧɟɡɚɜɢɫɢɦɵɟ ɞɢɫɤɪɟɬɧɵɟ ɫɥɭɱɚɣɧɵɟɜɟɥɢɱɢɧɵ ɩɪɢɧɢɦɚɸ
ɳɢɟɬɨɥɶɤɨɰɟɥɨɱɢɫɥɟɧɧɵɟɡɧɚɱɟɧɢɹZ X YɌɨɝɞɚ
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]