Still, I´m sorry :P, I don't see how this can be right. If I completely wright it out, I get
{\Bbb P}_\text{b}={\Bbb P}\left( {n = 1,{\text{ blue ball}}} \right) = \frac{b}{{r + b}}
{\Bbb P}_\text{r}={\Bbb P}\left( {n = 1,{\text{ red ball}}} \right) = \frac{r}{{r + b}}
{\Bbb...
I don't get it. What exactly is P(Bk)? The probability that B_n = k? And how can it be a sum of scaled probabilities? Because, all ready in the second turn, you would get a product of probabilities.
Say that p_b is the probability to draw a blue ball, p_bb to draw blue when blue is drawn in...
Well, I did have some progression before I went to my teachers.
The expectation value of the first turn is easy,
\begin{equation} \mathbb{E}\left[ {{B_1}} \right] = \frac{b}{{r + b}} \end{equation}.
And also it is not hard to find that
\begin{equation} \mathbb{P}\left[ {\left. {{B_n}...
Hi viraltux,
Well, sometimes when I get bored during lectures, I make up my own questions to see if I can answer them. And this one was quite hard. :P I asked some of my old teachers if they can give me some hints, but they couldn't give me an explicit expression either. For question 1 a...
Consider an urn with r red balls and b blue balls. In every turn, one ball is drawn.
When a red ball is drawn, it is put back in the urn together with some extra R red balls.
When a blue ball is drawn, it is left outside the urn.
The questions are:
1. What is the expectation value of...