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Math Help - help with solving equations using sigma notation

  1. #1
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    help with solving equations using sigma notation

    hello there!

    I would like som help with this problem

    Demonstrate using sigma notation that E(x+k)=E(x)+k

    Thanks in advance
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  2. #2
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    Quote Originally Posted by hello123 View Post
    Demonstrate using sigma notation that E(x+k)=E(x)+k
    Letís do it for a finite distribution.
    On \left\{ {x_1 ,x_2 , \cdots x_n } \right\} we know that \sum\limits_{k = 1}^n {P(x_k )}  = 1.

    So E(X + K) = \sum\limits_{k = 1}^n {P(x_k )} \left[ {x_k  + K} \right] = \sum\limits_{k = 1}^n {P(x_k )} \left[ {x_k } \right] + \sum\limits_{k = 1}^n {P(x_k )} \left[ K \right] = E(X) + K
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