Probability and Discrete Random Variables

Which term refers to events that cannot happen at the same time?

What is the term for the set of all possible outcomes of an experiment?

In probability theory, what do we call two events that have no outcomes in common?

Which rule states that the probability that either of two mutually exclusive events will occur is the sum of their individual probabilities?

What is the term for events whose occurrence or non-occurrence does not affect each other?

What is the term for an event that consists of more than one outcome happening together?

Which rule allows us to find the probability of either of two mutually exclusive events occurring?

What is the set of all possible outcomes of an experiment called?

In probability, what are events called when their occurrence has no effect on each other?

Which term refers to the probability that an event does not occur?

Events and Probability Rules

An event can be either a simple event or a compound event
A sample space is the set of all possible outcomes of an experiment
Mutually exclusive events are events that cannot occur simultaneously
Independent events are events where the occurrence of one event does not affect the probability of the other event
The Addition Rule is used to calculate the probability of the union of two events
The Complement Rule is used to calculate the probability of the complement of an event
The Intersection of events refers to the occurrence of two or more events simultaneously
Conditional events are events where the probability of one event is affected by the occurrence of another event

Discrete Random Variables

A discrete random variable exists if it satisfies two criteria:
- The variable can only take on a countable number of distinct values
- The variable can be defined using a probability mass function (PMF)
A probability mass function (PMF) is a function that assigns a probability to each possible value of a discrete random variable
A cumulative distribution function (CDF) is a function that assigns a probability to the set of values less than or equal to a given value of a discrete random variable
The expected value of a discrete random variable can be calculated using a formula
The variance and standard deviation of a discrete random variable can be calculated using a formula

Test your knowledge on concepts such as simple event, compound event, sample space, mutually exclusive events, independent events, addition rule, complement rule, and more. Understand the criteria for a discrete random variable to exist and learn about probability mass functions (PMF) and their applications.