# probability theory

1. ### How to evaluate Mean and Variance of Min Function??

Detail is Given in Image attach
2. ### Prove: Birth-death chain has stationary distribution -> satisfy detail bal. equations

I'm working my way through a course in stochastic processes but came across this Lemma in my coursebook where they didn't show the working (Lemma 8.5). I'm not familiar with doing proofs and it isn't taught in any of my courses but I can read/understand them, how did they reach the conclusion of...
3. ### Two events meeting

Hello everyone, I have a question regarding two events that take place randomly over a certain time period and meet. A similar problem would be phrased as follows, which is maybe simpler: Person A and person B each have 20 balls labelled 1 to 20. Person A picks n number of balls and person...
4. ### WANT Theoretical Probabilities theory books suggestion

Hello, I am reading a theoretical probability theory book " Probability Theory: The Logic of science " by E.T.Jaynes. But, this book is very advanced for me. I know the probability theory mathematically, but i want to feel the theories. So any suggestion on basic theoretical probabilities theory...
5. ### Find probability of the given data set, what probability i can say it is Bad.

I have a issue where there is a data set. and in there i have good and bad category, and in that category there are few elements that can be good and bad.... you can see the ven diagram i attached to get a view and the data set i have. please ill be really glad if you could help me out...
6. ### Probability calculation problem for a ranked set sample

Let us consider a case where a ranked set sampling scheme from $n^2$ subjects has been adopted. There are a total of $n$ RSS blocks. So each RSS block contains $n$ subjects. We will follow up them. Some of these subjects will fulfill a certain criterion and get a treatment and some will not be...
7. ### Need help calculating some values to be used in a cost/risk analysis

Hello, **If this is in the wrong forum, could someone tell me where it needs to be before removing it?**** I am needing some help calculating the possible profits I can make for producing certain amounts of 2 different products each month. (Modifying a basic jon boat and reselling it). The...
8. ### How to prove a non negative definite matrix has to be a variance-covariance matrix?

I know this is a iff condition,and the reverse is easy to prove.But I am having some difficulty to prove that all non negative definite matrices are variance covariance matrix.From what i have collected from wikipedia,I tried to prove it this way. Let A be a non negative definite matrix...
9. ### incremental Mutual information

Mutual information I computed Mutual information between two variables X and Y from data D at time t. I(X,Y) from D. Now at time t+1 new data arrived so, how i can estimate new value of MI using previous value rather than previous data. Thanks in advance.
10. ### Probability of a team making the finals

Hi, I am trying to find how to calculate the probability of "x" number of events happening within "y" opportunities. However each opportunity has a different probability. For example to calculate the probability of "TEAM WOW" winning 0, 1, 2, 3, or 4 games out of the 4 games they play...
11. ### π-system and monotone class

Assume P is a π-system (that is, P is closed under finite intersections) and M is monotone class (that is M is a non-empty collection of subsets of Ω closed under monotone limits). Show that P⊂M does not imply σ(P)⊂M.
12. ### sigma -fieled

Let X : \Omega \rightarrow R and F be a class of subsets of R. show \sigma(X^{-1} (F))=X^{-1}(\sigma(F)) where X^{-1} (F)={X^{-1} (A):A\in F}