Sea X una variable aleatoria continua con función de distribución F X. Obtener la distribución de...
14
b x b b | x | x b x b g(x) Sea X una variable aleatoria continua con función de distribución F X . Obtener la distribución de la variable aleatoria Y= g(X) en los siguientes casos: b | x | 0 b | x | x g(x) a) b) Solución a) Solución b) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial- NoDerivs 2.5 License.
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Transcript of Sea X una variable aleatoria continua con función de distribución F X. Obtener la distribución de...
b xb
b|x| x
b xb
g(x)
Sea X una variable aleatoria continua con función de distribución FX. Obtener
la distribución de la variable aleatoria Y= g(X) en los siguientes casos:
b|x| 0
b|x|x g(x)
a) b)
Solución a)
Solución b)
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
Solución a)
Solución b)
b xb
b|x| x
b xb
g(x)
b|x| 0
b|x|x g(x)
a) b)
Sea X una variable aleatoria continua con función de distribución FX. Obtener
la distribución de la variable aleatoria Y= g(X) en los siguientes casos:
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
Y es de tipo discreto
[
[
b xb
b|x| x
b xb
g(x)
y
y
(y)FY
-b
b
b
-b
[
[
0 y < -b
1 y b
-b y < b
(y)FY y)P(Y y]),(- P(Y
g(X)Y
y])),((-gP(X -1
y]),(-P(X
(y)F y)P(X X
(y)FX
x
y=g(x)
1
b-b y
FY
1(b)Fy 0b)(F XX Y es de tipo continuo
Y es de tipo mixto• En otro caso
•
bxb- c,(x)F X •
Valores –b y b, si 0<c<1
Degenerada en -b, si c=1
Degenerada en b, si c=01(b)Fb)(F0 XX
1(b)Fb)(F0 XX
1(b)Fb)(F0 XX
Y≡X
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
(y)FY
0 y < -b
1 y b
-b y < b (y)FX
Y es de tipo discreto bxb- c,(x)F X •
1(b)Fy 0b)(F XX Y es de tipo continuo
Y es de tipo mixto
•
b xb
b|x| x
b xb
g(x)
g(X)Y
• En otro caso
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
[
[
y
y
-b
b
b
-b
(y)FY y)P(Y y]),(- P(Y
g(X)Y
y])),((-gP(X -1
y]),(-P(X
(y)F y)P(X X
x
y=g(x)
b|x| 0
b|x|x g(x)
[
[
(y)FY
y < -b(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
-b
b
b
-b
y)P(Y ,-b])(- P(Y
g(X)Y
,-b]))((-gP(X -1
,-b])(-P(X
(-b)F -b)P(X X
x
y=g(x)
b|x| 0
b|x|x g(x)
[
[
(y)FY
y < -b
-b y < 0
(y)FX
(-b)FX
-b)P(Y
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
-b
b
b
-b
0)P(Y {0}) ,-b](- P(Y
g(X)Y
({0}))g ,-b])((-gP(X -1-1
b]),(-P(X
(b)F b)P(X X
x
y=g(x)
b|x| 0
b|x|x g(x)
[
[ [[
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
(-b)FX
y)P(Y
(b)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
(y)FY
-b
b
b
-b
y < -b
-b y < 0
y)P(Y y])[b,{0} ,-b](- P(Y
g(X)Y
y]))([b,g({0})g ,-b])((-gP(X -1-1-1
y]),(-P(X
(y)F y)P(X X
(y)FX
x
y=g(x)
b|x| 0
b|x|x g(x)
0 y < b
[
[y b
[
[
(-b)FX
(b)FX
y
[
[
y[
[(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
b|x| 0
b|x|x g(x)
g(X)Y
(b)Fb)(F XX • Y (≡ X) es de tipo continuo
1
b-b y
FY
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
y b
(-b)FX
(b)FX
(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
b|x| 0
b|x|x g(x)
g(X)Y
(b)Fb)(F XX • Y (≡ X) es de tipo continuo
(b)Fb)(F XX • b xsi (b)F(x)Fy b xsi (-b)F(x)F XXXX Y (≡ 0) es de tipo
discreto
1
b-b y
FY
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
y b
(-b)FX
(b)FX
(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
b|x| 0
b|x|x g(x)
g(X)Y
(b)Fb)(F XX • Y (≡ X) es de tipo continuo
(b)Fb)(F XX • b xsi (b)F(x)Fy b xsi (-b)F(x)F XXXX Y (≡ 0) es de tipo
discretoen otro caso Y es de tipo mixto
1
b-b y
FY
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
y b
(-b)FX
(b)FX
(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
b|x| 0
b|x|x g(x)
g(X)Y
(b)Fb)(F XX • Y (≡ X) es de tipo continuo
(b)Fb)(F XX • b xsi (b)F(x)Fy b xsi (-b)F(x)F XXXX Y (≡ 0) es de tipo
discretoen otro caso Y es de tipo mixto
1
b-b y
FY
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
y b
(-b)FX
(b)FX
(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
b|x| 0
b|x|x g(x)
g(X)Y
(b)Fb)(F XX • Y (≡ X) es de tipo continuo
(b)Fb)(F XX • b xsi (b)F(x)Fy b xsi (-b)F(x)F XXXX Y (≡ 0) es de tipo
discretoen otro caso Y es de tipo mixto
1
b-b y
FY
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
y b
(-b)FX
(b)FX
(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
b|x| 0
b|x|x g(x)
g(X)Y
(b)Fb)(F XX • Y (≡ X) es de tipo continuo
(b)Fb)(F XX • b xsi (b)F(x)Fy b xsi (-b)F(x)F XXXX Y (≡ 0) es de tipo
discretoen otro caso Y es de tipo mixto
(y)FY
y < -b
-b y < 0
(y)FX
0 y < b
y b
(-b)FX
(b)FX
(y)FX
BY: Grupo CDPYE-UGR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.
