In situations like this it's more common to model the systems as what are called stochastic processes, in this case probably Markov chains.
The binomial distribution is a discrete probability distribution. The number of possible outcomes depends on the number of possible successes in a given trial. For the Poisson distribution there are Infinitely many.
p
Each outcome must be classified as a success (p) or a failure (r),The probability distribution is discrete.Each trial is independent and therefore the probability of success and the probability of failure is the same for each trial.
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
A large sample (n > 25) and p, the probability of success on each trial = around 0.5 (0.35 to 0.65).Independence is already assumed for it to be binomial.A large sample (n > 25) and p, the probability of success on each trial = around 0.5 (0.35 to 0.65).Independence is already assumed for it to be binomial.A large sample (n > 25) and p, the probability of success on each trial = around 0.5 (0.35 to 0.65).Independence is already assumed for it to be binomial.A large sample (n > 25) and p, the probability of success on each trial = around 0.5 (0.35 to 0.65).Independence is already assumed for it to be binomial.
The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.
The binomial distribution is a discrete probability distribution. The number of possible outcomes depends on the number of possible successes in a given trial. For the Poisson distribution there are Infinitely many.
It depends on the trial, and is normally denoted by p.
What is the symbol for a Probability of success in a binomial trial?
p
Each outcome must be classified as a success (p) or a failure (r),The probability distribution is discrete.Each trial is independent and therefore the probability of success and the probability of failure is the same for each trial.
Suppose you have n trials of an experiment in which the probability of "success" in each trial is p. Then the probability of r successes is: nCr*pr*(1-p)n-r for r = 0, 1, ... n. nCr = n!/[r!*(n-r)!]
The letter p, in lower case.
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
No, in general is not. It is only symmetric if the probability of success in each trial is 0.5
The requirements are that there are repeated trials of the same experiment, that each trial is independent and that the probability of success remains the same.
In typical notation, "p" is the probability of sucess and "q" is the probability of failure. So q = 1 - p. But for your question: p = p.