All Questions
Tagged with sum binomial-distribution
5
questions
4
votes
2
answers
121
views
Confidence interval for the sum of 2 binomially distributed variables
$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure:
$k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and
$k_2 = 1000$ ...
- 41
1
vote
0
answers
357
views
Probability of sum of sequences of integers
Let K be a positive integer.Suppose that the integers 1,2,3,...,3k+1are written down in random order.What is the probability that at no time during this process, the sum of the integers that have been ...
- 1,216
3
votes
1
answer
74
views
Summation of combinations up to $r-1$ terms
I am trying to come up with a simplified expression for $$\sum_{k=r}^{n}\binom{n}{k}$$
Choosing $x=y=1$ in Binomial theorem, I have $$2^n = \sum_{k=0}^{n}\binom{n}{k}$$ $$2^n = \sum_{k=0}^{r-1}\binom{...
- 31
2
votes
1
answer
417
views
difference between independent binomial variables
Let $X_1$ and $X_2$ be independent random variables where $X_1 \sim \mathrm{Bin}(m, 1/2)$ and $ X_2 \sim \mathrm{Bin}(n,1/2)$.
How can we prove that $X_1 - X_2 + n \sim \mathrm{Bin}(m + n ,1/2)$?
Can ...
- 663
6
votes
1
answer
148
views
multi stage binomial "process"
I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution
$$
X_1 \sim \text B(K,p)
$$
, p is the ...
- 198