Module 2C Notes Flashcards
What is probability?
Probability is the numerical measure of the likelihood that an event will occur.
Define random experiment.
A random experiment is a process that generates well-defined outcomes.
What is sample space?
Sample space specifies all possible outcomes for a random experiment.
What is an event in probability?
An event is a collection of outcomes.
How is the probability of an event calculated?
The probability of an event is equal to the sum of the probabilities of the outcomes included in the event.
What is the complement of Event A?
The complement of Event A is the event that includes all outcomes not in Event A.
What does the union of events A and B represent?
The union of A and B is the event containing all outcomes belonging to A or B or both.
What are mutually exclusive events?
Mutually exclusive events are those where the occurrence of one event precludes the occurrence of the other.
What is conditional probability?
Conditional probability refers to the probability of an event given that another event has occurred.
What is Bayes’ Theorem used for?
Bayes’ Theorem is used to revise prior probabilities with new information to produce posterior probabilities.
Define a random variable.
A random variable is a numerical description of the outcome of a random experiment.
What are the two types of random variables?
Random variables can be classified as either discrete or continuous.
What is a discrete random variable?
A discrete random variable can assume only specified values.
What is a continuous random variable?
A continuous random variable can assume any numerical value in an interval or collection of intervals.
Give examples of continuous random variables.
Examples include time, weight, distance, and temperature.
What is a probability distribution?
A probability distribution describes the range and relative likelihood of possible values for a random variable.
What is a probability mass function?
Denoted by f(x) and provides the probability for each value of the random variable.
What is an empirical probability distribution?
An empirical probability distribution is generated from observations.
What is expected value in the context of random variables?
Expected value, or mean, is a measure of the central location for the random variable.
What does variance measure?
Variance measures the variability in the values of a random variable.
What is a discrete uniform probability distribution?
A discrete uniform probability distribution occurs when all possible values of the probability mass function are equal.
What characterizes a binomial probability distribution?
A binomial probability distribution describes a fixed number of independent trials with two possible outcomes: success and failure.
What two properties must a random variable meet to be described by the Poisson probability distribution?
- The probability of an occurrence is the same for any two intervals of equal length
- The occurrence or non-occurrence in any interval is independent of the occurrence or non-occurrence in any other interval.
What is the fundamental difference between discrete and continuous random variables?
Discrete random variables use a probability mass function for specific values, while continuous random variables use a probability density function for intervals.
What is a uniform probability distribution?
A uniform probability distribution occurs when every interval of a given length is equally likely.
List characteristics of the normal distribution.
- The highest point on the normal curve is at the mean, median, and mode
- The mean can be any numerical value
- Probabilities are given by the areas under the curve
- Total area under the curve is 1
- Standard deviation affects the width and flatness of the curve.
What does a larger standard deviation indicate in a normal distribution?
Larger values of the standard deviation result in wider, flatter curves, showing more variability in the data.
