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Given $mathbb E(5X+2)=12$ and $mathbb E(X|Y)=Y^3$ compute $mathbb E(Y^3)$



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Prove that $EX=E(E(X|Y))$Given $X$ and $Y$ are independent N(0,1) random variables and $Z = sqrtX^2+Y^2$ from the marginal pdf of $Z$Evaluate $mathbbE[e^e^x] =int_mathbbRe^e^xf(x)dx$, where $f(x)$ is Gaussian kernel.Given Max has probability p to win each game, compute the expected number of runs* after n gamesProbability Question. Prove that P(A|B) = P(A) given that P(A|B)= 0.52 and P(B)= 0.43Compute factorized and marginalized distribution of the graphFind $limsup_ntoinfty Y_n$ given the value of $mathbbE(limsup_ntoinfty Y_n)$Variance of random sum of random i.i.d. variables - spot the mistake?Conditional expectation with a third random variableConditional expectation of minimum of exponential random variablesConditional Expectation of a Sum of Random Variables and a Random Integer










3












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Given $mathbb E(5X+2)=12$ and $mathbb E(X|Y)=Y^3$ compute $mathbb E(Y^3)$.



I've been trying this a million different ways and can't seem to reach a final answer, I would love any suggestions!










share|cite|improve this question











$endgroup$











  • $begingroup$
    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial, and equation editing how-to
    $endgroup$
    – Fareed AF
    Mar 27 at 20:26















3












$begingroup$


Given $mathbb E(5X+2)=12$ and $mathbb E(X|Y)=Y^3$ compute $mathbb E(Y^3)$.



I've been trying this a million different ways and can't seem to reach a final answer, I would love any suggestions!










share|cite|improve this question











$endgroup$











  • $begingroup$
    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial, and equation editing how-to
    $endgroup$
    – Fareed AF
    Mar 27 at 20:26













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1



$begingroup$


Given $mathbb E(5X+2)=12$ and $mathbb E(X|Y)=Y^3$ compute $mathbb E(Y^3)$.



I've been trying this a million different ways and can't seem to reach a final answer, I would love any suggestions!










share|cite|improve this question











$endgroup$




Given $mathbb E(5X+2)=12$ and $mathbb E(X|Y)=Y^3$ compute $mathbb E(Y^3)$.



I've been trying this a million different ways and can't seem to reach a final answer, I would love any suggestions!







probability probability-theory conditional-expectation conditional-probability expected-value






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 27 at 20:31









callculus

18.9k31629




18.9k31629










asked Mar 27 at 20:23









LnicksLnicks

161




161











  • $begingroup$
    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial, and equation editing how-to
    $endgroup$
    – Fareed AF
    Mar 27 at 20:26
















  • $begingroup$
    Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial, and equation editing how-to
    $endgroup$
    – Fareed AF
    Mar 27 at 20:26















$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial, and equation editing how-to
$endgroup$
– Fareed AF
Mar 27 at 20:26




$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial, and equation editing how-to
$endgroup$
– Fareed AF
Mar 27 at 20:26










2 Answers
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$begingroup$

$$mathbb E(5X+2)=5,mathbb E(X)+2=12 implies mathbb E(X)=2$$



$$mathbb E(Y^3)=mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)=2$$






share|cite|improve this answer











$endgroup$








  • 2




    $begingroup$
    For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
    $endgroup$
    – Chase Ryan Taylor
    Mar 27 at 21:13



















2












$begingroup$

$E[X] = 2$.



Since $E[ X|Y] = Y^3$, then $E[Y^3] = E[ E[X|Y]] = E[X] = 2$.






share|cite|improve this answer









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    2 Answers
    2






    active

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    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    7












    $begingroup$

    $$mathbb E(5X+2)=5,mathbb E(X)+2=12 implies mathbb E(X)=2$$



    $$mathbb E(Y^3)=mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)=2$$






    share|cite|improve this answer











    $endgroup$








    • 2




      $begingroup$
      For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
      $endgroup$
      – Chase Ryan Taylor
      Mar 27 at 21:13
















    7












    $begingroup$

    $$mathbb E(5X+2)=5,mathbb E(X)+2=12 implies mathbb E(X)=2$$



    $$mathbb E(Y^3)=mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)=2$$






    share|cite|improve this answer











    $endgroup$








    • 2




      $begingroup$
      For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
      $endgroup$
      – Chase Ryan Taylor
      Mar 27 at 21:13














    7












    7








    7





    $begingroup$

    $$mathbb E(5X+2)=5,mathbb E(X)+2=12 implies mathbb E(X)=2$$



    $$mathbb E(Y^3)=mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)=2$$






    share|cite|improve this answer











    $endgroup$



    $$mathbb E(5X+2)=5,mathbb E(X)+2=12 implies mathbb E(X)=2$$



    $$mathbb E(Y^3)=mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)=2$$







    share|cite|improve this answer














    share|cite|improve this answer



    share|cite|improve this answer








    edited Mar 27 at 21:08









    Chase Ryan Taylor

    4,46221531




    4,46221531










    answered Mar 27 at 20:31









    Fareed AFFareed AF

    972112




    972112







    • 2




      $begingroup$
      For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
      $endgroup$
      – Chase Ryan Taylor
      Mar 27 at 21:13













    • 2




      $begingroup$
      For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
      $endgroup$
      – Chase Ryan Taylor
      Mar 27 at 21:13








    2




    2




    $begingroup$
    For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
    $endgroup$
    – Chase Ryan Taylor
    Mar 27 at 21:13





    $begingroup$
    For any readers: Reference this answer to see that $mathbb Ebigl(mathbb E(X|Y)bigr)=mathbb E(X)$.
    $endgroup$
    – Chase Ryan Taylor
    Mar 27 at 21:13












    2












    $begingroup$

    $E[X] = 2$.



    Since $E[ X|Y] = Y^3$, then $E[Y^3] = E[ E[X|Y]] = E[X] = 2$.






    share|cite|improve this answer









    $endgroup$

















      2












      $begingroup$

      $E[X] = 2$.



      Since $E[ X|Y] = Y^3$, then $E[Y^3] = E[ E[X|Y]] = E[X] = 2$.






      share|cite|improve this answer









      $endgroup$















        2












        2








        2





        $begingroup$

        $E[X] = 2$.



        Since $E[ X|Y] = Y^3$, then $E[Y^3] = E[ E[X|Y]] = E[X] = 2$.






        share|cite|improve this answer









        $endgroup$



        $E[X] = 2$.



        Since $E[ X|Y] = Y^3$, then $E[Y^3] = E[ E[X|Y]] = E[X] = 2$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Mar 27 at 20:34









        dnqxtdnqxt

        7625




        7625



























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