# Thread: Expected Value of Sigma of Geometrically distributed parameter y

1. ## Expected Value of Sigma of Geometrically distributed parameter y

What will be the expected value of the sum of geometrically distributed parameter y.

E [Sigma y]

2. the sum of the expectations OF the n different Y's.
IS the parameter Y?
Or are the random variables $\displaystyle Y_i$

3. y(i) are the random variables
The distribution of y(i) is Prob(y(i)=t)=p(i)*(1-p(i))^(t-1)

Thanks for the reply. Looking forward.

4. Originally Posted by himanshubahmani
What will be the expected value of the sum of geometrically distributed parameter y.

E [Sigma y]
You're notation is different than what my book has. But a geometrically distributed variable in my book is a negative binomial distribution and E(X)=$\displaystyle \frac{r(1-p)}{p}$ where r is the number of successes and p is the probability of success.

5. $\displaystyle E\left(\sum_{i=1}^nY_i\right) = \sum_{i=1}^nE(Y_i)$

where independence is not needed between the Y's.

SOME geo's start at 0 some start at 1.
It depends on your definition.
You might count the first trial or not.
That r is my n, the number of geo's that you're adding.
NOTE that if they are indep, then the sum is a neg bio.
BUT even if they are dependent then the expected value of the sum is still the sum of the expectations.