Need help with probability question. probability of dependent events.

  • Context: MHB 
  • Thread starter Thread starter Mewlove
  • Start date Start date
  • Tags Tags
    Events Probability
Click For Summary
SUMMARY

The discussion centers on calculating the probabilities of landing on various levels in a finite state Markov chain, specifically when transitioning between levels -1, 0, and 1 with defined probabilities. The user seeks to understand the steady state probability distribution for this system, which can be modeled using eigenvectors. The key to solving this problem lies in recognizing the periodic nature of the Markov chain, particularly when the number of levels (n) is even or odd. The recommended approach is to study the properties of finite state Markov chains to derive the necessary probabilities.

PREREQUISITES
  • Understanding of finite state Markov chains
  • Knowledge of eigenvectors and eigenvalues
  • Familiarity with probability theory
  • Concept of steady state probability distributions
NEXT STEPS
  • Study the properties of finite state Markov chains
  • Learn about eigenvector calculations in the context of Markov processes
  • Explore the concept of periodicity in Markov chains
  • Research steady state probability distributions and their applications
USEFUL FOR

Mathematicians, statisticians, data scientists, and anyone interested in probability theory and Markov processes will benefit from this discussion.

Mewlove
Messages
1
Reaction score
0
Would like to know what method, or distribution to use when solving a problem like this:I start from level 0. There is a probability p chance to drop to level -1 and a (1-p) chance to increase to level 1.

The levels range from level -n to level n. When it reaches level -n or level n, it resets back to 0 on the same cycle.
(Also, if you are at level -1, there is (1-p) chance to go back to level 0)

How do I calculate the percentage of landing on each level (not counting the reset), assuming I continue running this infinitely? Seems like dependent events. Is there any theorem or formula I can use?

Thanks!
 
Last edited:
Physics news on Phys.org
what you're looking for here is a finite state (recurrent, time homogenous) markov chain. Depending on whether your n is even or odd, the chain may actually be periodic with period 2 but that is a minor complication-- you want to solve for the eigenvector that gives a steady state probability distribution.

the key thing to search for is 'finite state markov chain'
 

Similar threads

MHB Calculating probability that 3 events occur 1 after other
  • · Replies 1 ·
Replies
1
Views
2K
Graduate A game of seemingly mutually independent events
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad What is the probability that the product of the digits is odd?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
4K
Undergrad Probability distribution of random events
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Probability paradox: P(X=x)=1/n >1
  • · Replies 5 ·
Replies
5
Views
3K
High School How to calculate this conditional probability?
  • · Replies 7 ·
Replies
7
Views
873
Graduate Runners in a race, probability paradox
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Help Needed: Probability Problem in Risk Management Calculcations
  • · Replies 4 ·
Replies
4
Views
2K
MHB Probability to get a chocolate snowman or a chocolate reindeer
  • · Replies 2 ·
Replies
2
Views
2K