Expected value of multiplication of two indicator random variables?

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I found the following statement in a book:



When $k neq j$ , the variables $X_ij$ and $X_ik$ are independent, hence




$E[X_ijX_ik] = E[X_ij]E[X_ik]$




where E is the expected value. Can anyone explain why this property applies and what would be the affect if $k = j$.




random-variables expectation




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    up vote
    -1
    down vote

    favorite












    I found the following statement in a book:



    When $k neq j$ , the variables $X_ij$ and $X_ik$ are independent, hence




    $E[X_ijX_ik] = E[X_ij]E[X_ik]$




    where E is the expected value. Can anyone explain why this property applies and what would be the affect if $k = j$.




    random-variables expectation




    share|cite|improve this question





















      up vote
      -1
      down vote

      favorite









      up vote
      -1
      down vote

      favorite











      I found the following statement in a book:



      When $k neq j$ , the variables $X_ij$ and $X_ik$ are independent, hence




      $E[X_ijX_ik] = E[X_ij]E[X_ik]$




      where E is the expected value. Can anyone explain why this property applies and what would be the affect if $k = j$.




      random-variables expectation




      share|cite|improve this question











      I found the following statement in a book:



      When $k neq j$ , the variables $X_ij$ and $X_ik$ are independent, hence




      $E[X_ijX_ik] = E[X_ij]E[X_ik]$




      where E is the expected value. Can anyone explain why this property applies and what would be the affect if $k = j$.





      random-variables expectation





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 6 at 16:03









      Jot Waraich

      104




      104




















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          We need to know how the $(X_ij)$ are defined to answer properly but you must know that for two indépendant variables, the expectation of the product is the product of the expectations.






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            active

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            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            3
            down vote



            accepted










            We need to know how the $(X_ij)$ are defined to answer properly but you must know that for two indépendant variables, the expectation of the product is the product of the expectations.






            share|cite|improve this answer

























              up vote
              3
              down vote



              accepted










              We need to know how the $(X_ij)$ are defined to answer properly but you must know that for two indépendant variables, the expectation of the product is the product of the expectations.






              share|cite|improve this answer























                up vote
                3
                down vote



                accepted







                up vote
                3
                down vote



                accepted






                We need to know how the $(X_ij)$ are defined to answer properly but you must know that for two indépendant variables, the expectation of the product is the product of the expectations.






                share|cite|improve this answer













                We need to know how the $(X_ij)$ are defined to answer properly but you must know that for two indépendant variables, the expectation of the product is the product of the expectations.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Aug 6 at 16:10









                Pjonin

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