umzung said:Homework Statement:: The number of items bought by each customer entering a bookshop is a random variable X that has a geometric distribution starting at 0 with mean 0.6.
Find the value of the parameter p of the geometric distribution, and hence write down the probability generating function of X.
Homework Equations:: $$q/(1-ps)$$
I know the p.g.f. of X is $$q/(1-ps)$$ and that the mean is $$p/q$$, but how do I find a specific value for p here?
$$p$$ is the probability, $$q$$ is (1 - probability) and $$s$$ is a dummy variable, not a random variable.PeroK said:What are ##p, q## and ##s## here?
Okay, so the mean is ##q/p = (1-p)/p##. Do you know the mean in this case?umzung said:$$p$$ is the probability, $$q$$ is (1 - probability) and $$s$$ is a dummy variable, not a random variable.
Geometric distribution is a type of probability distribution that models the number of trials needed to achieve a success in a series of independent trials with a constant probability of success. It is often used in situations where there are only two possible outcomes, such as success or failure.
To find a specific p value using geometric distribution, you would need to know the number of trials, the probability of success on each trial, and the desired number of successes. Then, you can use the formula P(X = k) = (1-p)^(k-1) * p, where k is the desired number of successes, to calculate the probability of getting exactly k successes in the given number of trials.
The mean of geometric distribution is equal to 1/p, where p is the probability of success on each trial. In other words, the mean represents the average number of trials needed to achieve a success.
Geometric distribution is different from other probability distributions in that it only has two possible outcomes (success or failure) and the probability of success remains constant for each trial. Other distributions, such as binomial distribution or normal distribution, can have more than two outcomes and/or varying probabilities of success.
Geometric distribution is commonly used in situations where there are a fixed number of trials with a constant probability of success, such as in flipping a coin, rolling a die, or pulling cards from a deck. It can also be used in quality control processes, where a product is tested multiple times until it meets a certain standard. Additionally, it can be used in fields such as finance and biology to model the likelihood of success or failure in a series of events.