Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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2
votes
0answers
100 views
+250

Convergence of empirical distribution from another observations

Let $$(X_1,Y_1),\dots,(X_n,Y_n)$$ are i.i.d. observation with continuous distribution function $F=(G,H)$ such that $\Phi^{-1}(G)=a\Phi^{-1}(H)$ for some unknown value of $a$ where ...
19
votes
1answer
278 views
+250

Zombie outbreak on a $k$-regular graph

Suppose we have a zombie outbreak on a connected $k$-regular graph of order $n$. There are $n_0$ initially infected zombie nodes, and each turn, each zombie infects its neighbors with probability ...
1
vote
1answer
24 views
+50

Easy way to compute $Pr[\sum_{i=1}^t X_i \geq z]$

We have a set of $t$ independent random variables $X_i \sim Bin(n_i, p_i)$. We know that $$Pr[X_i \geq z] = \sum_{j=z}^{\infty} { n_i \choose j } p_i^j (1-p_i)^{n_i -j}.$$ But is there an easy way to ...