different between stochastic model and deterministic model using formula

Answer 1

A stochastic model is a mathematical model that incorporates randomness or uncertainty in its inputs or outputs. It takes into account probabilistic factors and includes random variables to represent uncertain quantities. The model's outputs are not deterministic, but rather represent a range of possible outcomes based on probability distributions.

On the other hand, a deterministic model is one in which the outcomes are completely determined by the inputs and parameters of the model. It does not consider randomness or uncertainty, and the results are calculated based on pre-defined relationships and equations.

To illustrate the difference mathematically, let's consider a simple example:

1. Stochastic Model:
Suppose we have a stochastic model to predict the number of customers that will visit a store in a day. Let's assume that the average number of customers (lambda) is 50 per day, and it follows a Poisson distribution. The formula for the probability mass function of a Poisson distribution is:
P(X=k) = (e^(-lambda) * lambda^k) / k!

Here, the number of customers (X) is a random variable, and the output of the model will be a probability distribution representing the possible number of customers each day.

2. Deterministic Model:
Now, let's consider a deterministic model to predict the number of days required to complete a project based on its estimated duration (D) in days and the number of resources (R) available. Suppose the formula to calculate the duration is:
Duration = D / R

Here, the output of the model is a single value representing the exact number of days required to complete the project. There is no randomness or uncertainty involved, as the result is solely determined by the inputs.

In summary, the main difference between stochastic and deterministic models is that stochastic models consider randomness and uncertainty, leading to a range of possible outcomes, while deterministic models do not incorporate randomness and provide a single, definitive outcome.