# help with solving equations using sigma notation

• Nov 13th 2009, 04:58 AM
hello123
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

• Nov 13th 2009, 08:18 AM
Plato
Quote:

Originally Posted by hello123
Demonstrate using sigma notation that E(x+k)=E(x)+k

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