|
2
|
Suppose we have a family $F_0,F_1,\dots$ of independent random variables which take the value $1$ with probability $p$ and $0$ otherwise; let $\delta$ be a number between $0$ and $1$. Let $X_n = \sum_{k=0}^n \delta^{n-k} F_k$. I'm interested in the distribution of $X_n$. It seems straightforward enough to be known and have a name - does anybody know what it is? |
|||||||||
|
|
3
|
Unless I misunderstood your intention (see my comment above), if you take $n=\infty$ you get a Bernoulli convolution. See the paper Sixty Years Of Bernoulli Convolutions by Peres, Schlag and Solomyak which can also the last paper here. |
|||||||||
|
|
0
|
It is a finite distribution over numbers which aren't necessarily integers. I wouldn't expect it to have a name. |
|||
|
|
