# Search results for query: *

1. ### Independence of events question

Oh I've made a mistake I get it now : ##\bigcap_{j\in J} B_j = A\cap B^c = A - A\cap B## with ##A = \bigcap_{j\in J_1} A_j## and ##B = \bigcup_{j\in J_2} A_j ## we have ## A \cap B = \bigcup_{j\in J_2} \bigcap_{k\in J_1} (A_k \cap A_j) ## And with the principle of inclusion exclusion and the...
2. ### Independence of events question

Hello, I am studying independence of events and I came across a formula that I don't understand. It is rather technical, not very interesting, but I feel stuck and it stays in my mind. Could you explain the following : If ## (A_i)_{i\in I}## is a sequence of independent events on...
3. ### Lower Bound on Binomial Distribution

I am not competent to answer you about Chernoff bound, I don't know much about probabilities. There is an easy lower bound that is ##\epsilon^N## since you are summing positive terms.
4. ### Lower Bound on Binomial Distribution

I believe your expression tends to 0 as ##n \rightarrow \infty##, but I may be mistaking: Since ##0<\epsilon \le 0.001##, you get that ##0 < \epsilon^k \le \epsilon^{floor(N/2)+1} \le \epsilon ^{N/2}## and ## 0 < (1-\epsilon)^{N-k} \le 1 ## So that ##0\le \sum_{k=floor(N/2)+1}^N{N\choose...