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Results tagged with probability-distributions
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user 48831
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
4
votes
Accepted
The probability density function of the number of coins to first fill one box of $N$
(I change notation from $N,C$ to $n,c$ since I use capitals throughout to denote rvs).
Let $X_i$ be the random variable "number of the box the $i$-th coin", then $X_1,X_2,\ldots$ is an i.i.d. sequenc …
- 3,255
0
votes
Coupon collector targeting a collection among many
There a well known generating function methods (the ''symbolic method'' and ''Poissonization'') which can be used to deal with this kind of question.
However, I am unable to point to a reference for …
- 3,255
1
vote
Minimizer of two random walks
The topic belongs to the fluctuation theory
of random walks. See e.g. Feller II, 2nd ed. (1970), chapter XII.
Here is some useful (condensed) information:
(1) (for each $n$) the position of the (fi …
- 3,255
1
vote
Accepted
Suggestions for dealing with the "timed" balls-into-bins model
(I use the notation from my comments). By symmetry, $$\mathbb{P}(E^c)={n \choose m}\,\mathbb{P}(E^c, B=\{1,\ldots,m\})\;\;.$$
If $D_1=M_m\;\;$ we have to compute $$I_1:=\mathbb{P}(D_1^\prime>t+M_m,D_ …
- 3,255
1
vote
Accepted
Total progeny of a Galton-Watson branching process - standard textbook question
The answer above is fine, nevertheless I make some hopefully useful supplementary remarks (the first two essentially reformulating Did's answer)
(1) It is well known (see e.g. Feller I, 3rd ed., p.29 …
- 3,255
0
votes
The min of the mean of iid exponential variables
(Since you are looking for a reference, I turn my comment above into an answer:)
A proof using classical fluctuation theory is given my answer to
Expected supremum of average?
(I'm not aware that this …
- 3,255
3
votes
Accepted
How to calculate $P(\sum_{i=1}^{m}(A_i+S_i)\le L)$ with $A_i,L\sim\text{exp}(\lambda),S_i\si...
Call the left resp. right hand sum $R_m$ resp. $R_{m+1}$. As $L$ is $\exp(\lambda)$ and independent of $(R_m,R_{m+1})$ , taking expection with resp. to $L$ first gives
$$\mathbb{P}(R_m\leq L < R_{m+1 …
- 3,255