4.1: Probability, Sample Spaces, and Probability models Flashcards
What is probability in the context of uncertainty?
Probability is a number that measures the chance or likelihood that an event will occur, always between 0 and 1.
What is a sample space in the context of experiments?
A sample space is the set of all possible outcomes for an experiment.
Define a probability model.
A probability model is a mathematical representation of a random phenomenon.
What does the probability of an event being 0 or 1 signify?
A probability of 0 means the event will not occur, while a probability of 1 means the event is certain to occur.
What are the three methods for assigning probabilities to sample space outcomes?
The classical method, the relative frequency method, and the subjective method.
Describe the classical method of assigning probabilities.
Probabilities are assigned based on the assumption that each outcome in the sample space is equally likely.
What is the relative frequency method of assigning probabilities?
Probabilities are estimated based on the proportion of times the outcome occurs in a large number of trials.
Explain the subjective method of assigning probabilities.
Probabilities are based on intuition, experience, or expertise rather than long-run frequency.
What is the significance of P(E) in probability?
P(E) represents the probability of a sample space outcome E occurring.
How do probability models relate to random variables?
Probability models calculate probabilities for various events, which can include defining random variables that are numeric outcomes of experiments.
What are the two types of probability distributions?
Discrete probability distributions and continuous probability distributions.
Name two important discrete probability distributions.
The binomial distribution and the Poisson distribution.
Name two important continuous probability distributions.
The normal distribution and the exponential distribution.
