How to prove that exponential of an expected value of a variable is less than the expected value of the...












0














I am trying to prove the following:



$e^{E(x)} le E(e^x)$ for a discrete random variable x.



I am stuck on how to proceed. None of the usual rules for expected value seem to apply for something like $f(E(x))$. Can I some help? Thanks!!






expected-value







share|cite|improve this question













closed as off-topic by max_zorn, NCh, amWhy, Shailesh, John B Dec 1 at 0:44


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – max_zorn, NCh, amWhy, Shailesh, John B

If this question can be reworded to fit the rules in the help center, please edit the question.













  • Have you ever heard of Jensen's inequality( en.wikipedia.org/wiki/Jensen%27s_inequality)?
    – Seewoo Lee
    Nov 24 at 3:16










  • THANKS!! THIS IS JUST WHAT I NEEDED!
    – William Deng
    Nov 24 at 3:21
















0














I am trying to prove the following:



$e^{E(x)} le E(e^x)$ for a discrete random variable x.



I am stuck on how to proceed. None of the usual rules for expected value seem to apply for something like $f(E(x))$. Can I some help? Thanks!!






expected-value







share|cite|improve this question













closed as off-topic by max_zorn, NCh, amWhy, Shailesh, John B Dec 1 at 0:44


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – max_zorn, NCh, amWhy, Shailesh, John B

If this question can be reworded to fit the rules in the help center, please edit the question.













  • Have you ever heard of Jensen's inequality( en.wikipedia.org/wiki/Jensen%27s_inequality)?
    – Seewoo Lee
    Nov 24 at 3:16










  • THANKS!! THIS IS JUST WHAT I NEEDED!
    – William Deng
    Nov 24 at 3:21














0












0








0







I am trying to prove the following:



$e^{E(x)} le E(e^x)$ for a discrete random variable x.



I am stuck on how to proceed. None of the usual rules for expected value seem to apply for something like $f(E(x))$. Can I some help? Thanks!!






expected-value







share|cite|improve this question













I am trying to prove the following:



$e^{E(x)} le E(e^x)$ for a discrete random variable x.



I am stuck on how to proceed. None of the usual rules for expected value seem to apply for something like $f(E(x))$. Can I some help? Thanks!!






expected-value




expected-value






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 24 at 3:10









William Deng

32




32




closed as off-topic by max_zorn, NCh, amWhy, Shailesh, John B Dec 1 at 0:44


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – max_zorn, NCh, amWhy, Shailesh, John B

If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by max_zorn, NCh, amWhy, Shailesh, John B Dec 1 at 0:44


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – max_zorn, NCh, amWhy, Shailesh, John B

If this question can be reworded to fit the rules in the help center, please edit the question.












  • Have you ever heard of Jensen's inequality( en.wikipedia.org/wiki/Jensen%27s_inequality)?
    – Seewoo Lee
    Nov 24 at 3:16










  • THANKS!! THIS IS JUST WHAT I NEEDED!
    – William Deng
    Nov 24 at 3:21


















  • Have you ever heard of Jensen's inequality( en.wikipedia.org/wiki/Jensen%27s_inequality)?
    – Seewoo Lee
    Nov 24 at 3:16










  • THANKS!! THIS IS JUST WHAT I NEEDED!
    – William Deng
    Nov 24 at 3:21
















Have you ever heard of Jensen's inequality( en.wikipedia.org/wiki/Jensen%27s_inequality)?
– Seewoo Lee
Nov 24 at 3:16




Have you ever heard of Jensen's inequality( en.wikipedia.org/wiki/Jensen%27s_inequality)?
– Seewoo Lee
Nov 24 at 3:16












THANKS!! THIS IS JUST WHAT I NEEDED!
– William Deng
Nov 24 at 3:21




THANKS!! THIS IS JUST WHAT I NEEDED!
– William Deng
Nov 24 at 3:21










1 Answer
1






active

oldest

votes


















0














Exponent is a convex function. Use, as suggested in the comments, Jensen's inequality






share|cite|improve this answer





















  • Thanks! Just what I needed.
    – William Deng
    Nov 24 at 3:29


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














Exponent is a convex function. Use, as suggested in the comments, Jensen's inequality






share|cite|improve this answer





















  • Thanks! Just what I needed.
    – William Deng
    Nov 24 at 3:29
















0














Exponent is a convex function. Use, as suggested in the comments, Jensen's inequality






share|cite|improve this answer





















  • Thanks! Just what I needed.
    – William Deng
    Nov 24 at 3:29














0












0








0






Exponent is a convex function. Use, as suggested in the comments, Jensen's inequality






share|cite|improve this answer












Exponent is a convex function. Use, as suggested in the comments, Jensen's inequality







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 24 at 3:18









Makina

1,163115




1,163115












  • Thanks! Just what I needed.
    – William Deng
    Nov 24 at 3:29


















  • Thanks! Just what I needed.
    – William Deng
    Nov 24 at 3:29
















Thanks! Just what I needed.
– William Deng
Nov 24 at 3:29




Thanks! Just what I needed.
– William Deng
Nov 24 at 3:29



-

Popular posts from this blog

Plaza Victoria

Image
Plaza Victoria Plaza Victoria en 2017 Otros nombres Plaza de La Victoria Localización El Almendral, Valparaíso, Chile Vías adyacentes Chacabuco, Molina, Plaza Victoria y Edwards Creación 1841 Metro Bellavista Ubicación 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 Coordenadas: 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 [editar datos en Wikidata] La Plaza Victoria , también llamada Plaza de la Victoria , [ 1 ] ​ es una plaza ubicada en el sector El Almendral del plan de la ciudad de Valparaíso, Chile, de importancia patrimonial, que incluye valiosas estatuas y especies vegetales. [ 2 ] ​ La plaza se creó como tal en la primera mitad del siglo XIX, tomando previamente los nombres de Plaza Nueva y Plaza de Orrego . Si bien desde sus inicios tuvo relevancia histórica, no fue sino a partir de fines de los años 1860 cuando comenzó a cobrar mayor importancia y se convirtió en uno de los principales centros sociales de l...
Read more

Puebla de Zaragoza

Image
Para otros usos de este término, véase Puebla (desambiguación). Heroica Puebla de Zaragoza Localidad De arriba a abajo de izquierda a derecha: Estrella de Puebla, Volcán Popocatépetl, Catedral de Puebla, Monumento a Ignacio Zaragoza, Estadio Cuauhtémoc, Angelópolis y Vista panorámica de la ciudad. Escudo Otros nombres: El relicario de América/ La ciudad de los Ángeles/ La Angelópolis Lema: Muy noble y muy leal ciudad de Puebla de los Ángeles Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en México Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en Puebla Mapa interactivo Coordenadas 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Coordenadas: 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Idioma oficial Español Entidad Localidad  • País   México  • Estado Puebla  • Municipio Puebla Presidente municipal Claudia Rivera Vivanc...
Read more

Musa

Image
Para el género de plantas, véase Musa (planta). Apolo y la Nueve Musas En la mitología griega, las musas (en griego antiguo μοῦσαι « mousai» ) son, según los escritores más antiguos, las divinidades inspiradoras de las Artes: cada una de ellas está relacionada con ramas artísticas y del conocimiento. Son hijas de Zeus y de Mnemósine, compañeras del séquito de Apolo, dios olímpico de la música y patrón de las bellas artes, quien tuvo romances con cada una de ellas, dejando descendientes. Bajaban a la tierra a susurrar ideas e inspirar a aquellos mortales que las invocaran. En la época más arcaica eran las ninfas inspiradoras de las fuentes, en las cuales eran adoradas. Finalmente, alrededor de los siglos VIII-VII a. C. [ 1 ] ​ prevaleció en todo el territorio de la Hélade la adoración de las nueve Musas, que son Calíope, Clío, Erato, Euterpe, Melpómene, Polimnia, Talía, Terpsícore y Urania. El culto a las musas era originalmente de Tracia y Beocia, y fueron de vital impo...
Read more