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







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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

1,088115




1,088115












  • 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



-

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