2.1.0 Whats are Random Variables? Flashcards
What is a random variable?
A variable whose value is subject to variations due to randomness.
What are the two types of random variables?
Discrete and continuous random variables.
What is a discrete random variable?
A random variable that takes values from a specific set of countable values (e.g., integers).
What is a continuous random variable?
A random variable that takes numerical values within a specified interval or collection of intervals.
Give an example of a discrete random variable.
The roll of a fair die, which can only take integer values from 1 to 6.
Give an example of a continuous random variable.
The amount of snowfall in inches during winter, which can take any real value.
How are random variables denoted?
With capital letters, such as (X) or (Y).
How do random variables relate to sample spaces?
A random variable assigns a value to each element in the sample space.
What is an event in relation to a random variable?
An event is created by specifying a value or range of values for a random variable.
Give an example of an event formed from a random variable.
If (X) is the number of heads in four coin tosses, then (X = 3) is the event of getting exactly three heads.
What is a realization of a random variable?
An observed value of a random variable, denoted with lowercase letters (X = x) or (Y =y).
What are the two main components of a random variable?
The possible values (range or domain) and the probability distribution (representation of the function as a whole).
How are possible values presented for discrete random variables?
As a list of values (e.g., 0, 1, 2,…, 100).
How are possible values presented for continuous random variables?
As intervals (e.g., [0, 100]).
What is a probability distribution?
A function that assigns a probability to each possible value (or range) of a random variable.
