Probability geometric series summation

Asked Oct 10 '19 at 05:14

Active Oct 10 '19 at 06:14

Viewed 31 times

Suppose $ \sim (_1)$ on $\{1, 2, 3, \dots\}$, $ \sim (_2)$ on $\{1, 2, 3, \dots \}$, and ⊥ . Let $ = + $. Find $( = )$ under each condition.

a) Assume $ = _1 = _2$.

b) Assume $_1 \neq _2$. After setting up your summation, identify $, $ and $$ in a finite geometric series using the below formula and evaluate your summation.

$$ + + ⋯ + ^{(−1)} = \frac{(1 − ^)}{ 1 - r}$$

EDIT: So part a) so far I know I should use negative binomial distribution for part a (# of trials until 2 successes). So I could use the formula $\binom{x-1}{r-1}\cdot p ^ r \cdot (1 - p)^{(x - r)}$ with $r = 2$. But I don't know how to continue from that.

edited Oct 10 '19 at 06:14

callculus42

31,012

asked Oct 10 '19 at 05:14

aaaaaaaa

you need to show attempts of solution. people will not / shall not do your homework for you, but rather help with the experienced difficulties – Elen Khachatryan Oct 10 '19 at 05:19
I updated my thought process so far. – aaaaaaaa Oct 10 '19 at 05:26
please use latex notation when posting; I will edit your question now, but you should do it in the future – Elen Khachatryan Oct 10 '19 at 05:28
and again, you are not showing any steps, proceed to the implementation of the steps you are suggesting – Elen Khachatryan Oct 10 '19 at 05:31
@aaaaaaaa For a) see here and for b) see here . – callculus42 Oct 10 '19 at 06:13

Probability geometric series summation

0 Answers0