Need help with probability question. probability of dependent events.

In summary, the conversation discusses using a finite state markov chain to calculate the percentage of landing on each level in a problem where there is a chance to drop or increase levels. The key is to solve for the eigenvector that gives a steady state probability distribution. The chain may be periodic with period 2 depending on the value of n.
  • #1
Mewlove
1
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!
 
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  • #2
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'
 

What is the definition of dependent events?

Dependent events are events where the outcome of one event affects the outcome of another event. In other words, the probability of the second event occurring is dependent on the outcome of the first event.

How do you calculate the probability of dependent events?

The probability of dependent events can be calculated by multiplying the probability of the first event by the probability of the second event, given that the first event has already occurred. This can be represented by the formula P(A and B) = P(A) * P(B|A), where P(A) is the probability of event A and P(B|A) is the probability of event B given that event A has already occurred.

What is the difference between dependent and independent events?

The main difference between dependent and independent events is that the outcome of one event affects the outcome of the other in dependent events, while the outcome of one event has no effect on the outcome of the other in independent events. In other words, the probability of the second event occurring is not dependent on the outcome of the first event in independent events.

Can dependent events have a probability of 0?

Yes, dependent events can have a probability of 0. This means that the outcome of the first event makes it impossible for the second event to occur. For example, if the first event is rolling a 6 on a die and the second event is rolling a 7 on the same die, the probability of both events occurring is 0 because it is impossible to roll a 6 and a 7 on a single die.

How can you identify dependent events?

You can identify dependent events by looking at whether the outcome of one event affects the outcome of the other. If the outcome of the first event changes the probability of the second event occurring, then the events are dependent. Additionally, if the events are not mutually exclusive (i.e. they can occur at the same time), then they are likely dependent events.

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