03.Probability distributions Flashcards
what can we do with probability distribution?
We can use probability in operations management in areas in inventory management, resources planning, infrastructure/organisation, level of service (how satisfied are the customer).
How can we use probability for measurement ?
Measurements are when we are quantifying the evaluation criteria. E.g. in hotel reservation, we are testing what is the possibility that the time taken to perform the task will be under 6 mins as the CTQ requires.
whta is random variables and 2 types of it?
It is a value associated with the outcomes of an experiment. E.g. The number of guests that come to your hotel every day.
Discrete random variable can only have discrete variables (finite or infinite sequence)
e.g. Roll of a dice, number of cars in a parking, number of customers that enter a bank in one hour.
Continuous random variable can take any value in one or several intervals. E.g. age of EHL students, weight of a can, travel time between Geneva and Paris.
Probability mass function Vs Densitiy funciton?
Mass funciton is for discrete random variables, unrelated to one another. E.g., How many people came in to the shop today per hour, 2 people at 8, 12 people at 9, it is not continoues.
But density funciton is for continuous interval, e.g., probability of a ehl student between age 18 to 22?
differences between Cumulative discret random variable and continous random variable?
- For a discrete random variable, it is the sum of the probabilities of the outcomes less than or equal to x
- For a continuous random variable, it is the area under the probability density function.
what is mean? and what’s another name for it?
also called the expected value, the weighted average of all possible values of a random variable. Also called the expected value.
Weights are the probabilities of the values of the random variable.
The mean gives the central location of a random variable
what is variance
measure of the dispersion or variability of the possible values of the random variable. From the mean, how widely spread out the data is from the mean.
what is standard deviation?
is the positive square root of the variance.
- It is a measure of how far away the values of your random variable can be from the mean
WHat is the normal distribution?
the most widely used continous random distribution in practice.
It’s a bell curve, symmetricall around its mean.
What is a poisson distribution
Define: is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.[1] The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume. i.e. it must be random and it has to be discrete (cant be 2.2 persons has to be 2 or 3 persons.
- Number of phone calls received at the reception desk per hour
- Number of customers coming to your restaurant per day.
what is the properties of the poisson distribution?
- The probability of outcomes occurring in one-time interval is the same for two-time intervals equal in length (e.g. 1 hour, 1 day)
- The number of occurrences or the non-occurrence in one interval is independent than the number of occurrences or non-occurrences in another interval (e.g. a lot of customers today doesn’t imply a lot of customers tomorrow)
- we assume that the random hour we pick can represent the rest of hours.
What is exponential distribution
Continuous random variable that is used for the time needed to complete a task. I.e. the probability distribution of time between events in a Poisson point
What is an example/phenomen that is exponential distributed
The Poisson and Exponential probability distributions can be used to analyse a similar phenomenon:
- If the number of arrivals per hour are distributed following a Poisson distribution
- The time between two arrivals is then exponentially distributed
