After randomly generating five numbers with a geometric distribution and probability of 25%, I got { 1, 2, 0, 3, 5 } (I used rgeom(5, 0.25) in R to generate these numbers).
To find the Expected values, I believe it is just the mean of these 5 numbers, which is
E[x] = (1 + 2 + 3 + 5) / 5 = 11/5
But then, How would you find the variance for this? Specifically, E[x^2] since
var(x) = E[x^2] - E[x]^2
I don't really understand/know what it is i need to square. Usually, I would do ∑(c^2) * (p) for E[x^2] but idk if c $\in$ {1,2,3,0,5} in this case.
Hint:
For discrete case,
$$\mathbb{E}(X^2)=\sum_{x}x^2p(x)$$,
then use the variance formula.