hello there!
I would like som help with this problem
Demonstrate using sigma notation that E(x+k)=E(x)+k
Thanks in advance
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 $\displaystyle E(X + K) = \sum\limits_{k = 1}^n {P(x_k )} \left[ {x_k + K} \right] = \sum\limits_{k = 1}^n {P(x_k )} \left[ {x_k } \right] + \sum\limits_{k = 1}^n {P(x_k )} \left[ K \right] = E(X) + K$