Week 5- Randomness, Conditional Probability and Independence Probability,Simulation, Probability Rules Flashcards
Probability
A number between 0 and 1 that describes the proportion of times an outcome will occur in a very long series of repetitions. the likelihood of events occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 a certain event.
Law of Large Numbers
Says that the proportion of times a particular outcome will occur
approaches a single number (its probability) over a very large number of trials. a sample size gets closer to the average of the whole population as it grows because the sample is more representative of the population as it becomes larger.
Simulation
Imitation of a chance behavior, most often carried out with random numbers. Using computer experiments to mimic real-world scenarios or data-generating processes, allowing for the exploration of statistical methods and the estimation of probabilities when analytical solutions are difficult or impossible.
Sample Space (S)
The set of all possible outcomes of a chance process. The set of all possible outcomes of a random experiment, often represented using set notation { }.
Probability Model
A description of a chance process that consists of two parts: a sample space S, and a probability for each outcome. a mathematical representation of a random phenomenon, describing the likelihood of different outcomes by assigning probabilities to each event within a sample space. a convenient way to describe the distribution of the outcomes of an experiment. It consists of all the possible outcomes of an experiment their corresponding probabilities. It is often useful to display the probability model with a table.
Event
any collection of outcomes from some chance process; a subset of the sample space; usually denoted by letters such as A, B, C, etc. an event is a subset of the sample space (all possible outcomes) to which a probability is assigned. It represents a specific outcome or a collection of outcomes from a random experiment.
Mutually Exclusive (Disjoint)
Two events are mutually exclusive (or disjoint) if they have no outcomes in common and therefore cannot occur together. “Mutually exclusive” (also known as “disjoint”) events are those that cannot occur simultaneously; if one event happens, the other cannot.
Conditional Probability
Measures the likelihood of an event happening, knowing that another event has already taken place. . he probability of an event (A) occurring, given that another event (B) has already occurred, and is denoted as P(A|B), read as “the probability of A given B
Independent Events
Two events are independent if the occurrence of one event has no effect
on the chance that the other event will happen. Events where the outcome of one event doesn’t influence the probability of the other event occurring, meaning knowing one event happened doesn’t change the likelihood of the other.
