confused with wording of probability questions

[Jason12]

I'm not sure where to start with many probability questions because I don't understand what the question is asking me to do. Can someone tell me for what kinds of questions do you use binomial, markov chains, steady state, Bernoulli sequences, etc. and for what types of events (i.e. if they want an event in the future)

[keltingmeith]

Firstly, what you want to do is write out all the probabilities you have.

For example, "on any given day, the probability of Ben making his bus on time is 0.9. If B=the event Ben makes his bus on time, find the probability that Ben makes it to his bus 5 days in a row"

Well, you have two probabilities, and . Since you have one of two possibly choices - getting a heads and not getting a heads - this is a binomial distribution.

After you've done that, consider the exact situations you have, and think about if they affect the probabilities you've already written.

Next example, "if Ben misses his bus one day, the probability of making it the next day is 0.9. If he makes it on time to the bus, the probability of his missing it the next day is 0.15. If the first situation holds for Monday, find the probability that Ben makes it to his bus on Friday."

Well, now we have two probabilities again, but they're conditional. and . This implies that they might be a markov chain.

If you still have trouble, really think about all the situations that you can use each distribution you know:

-General discrete model, they give you ALL the information. It could be Bernoulli, it could be Markov, it could even be a distribution you don't know about, like Poisson or geometric. It doesn't matter, they gave you all the information, so just use that information. Don't worry about anything else.

-Binomial models. You either win, or you lose. If you're looking at a situation where the person either wins or loses, it's binomial.

-Markov chains. Often, it seems like you either win or lose, but there's a catch - time is always involved. If there's time involved, and you have conditional probabilities, it's a Markov chain.

-Steady states. These are just a special example of markov chains, where they want to know what it happens "over time", or "in the long run". If they ask something that sounds like they want to know about what will happen in the long term or after a long period of time, they want the steady state solution.

-Normal distributions, they'll tell you that something is normally distributed, every time. They'll then give you enough information such that if you don't know the mean or standard deviation (i.e. they didn't tell you), you can figure it out.

[Jason12]

if a question asks for the steady state probability do they want you to get the transition matrix to high powers (e.g. ^20, ^50) until the probability is constant or do they want you to use the formulas like b/(b+c)?

[keltingmeith]

Both will give the exact same result, so do whatever works for you.