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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- Nov 13th 2009, 03:58 AMhello123help 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 - Nov 13th 2009, 07:18 AMPlato
Let’s do it for a finite distribution.

On $\displaystyle \left\{ {x_1 ,x_2 , \cdots x_n } \right\}$ we know that $\displaystyle \sum\limits_{k = 1}^n {P(x_k )} = 1$.

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