Discrete Random Variables A discrete random variable is a variable that can take on a finite number of possible values. Examples of discrete random variable...
Discrete Random Variables
A discrete random variable is a variable that can take on a finite number of possible values. Examples of discrete random variables include the number of heads or tails in a coin toss, the number of students in a classroom, or the number of defects in a manufactured product.
The probability mass function (PMF) of a discrete random variable defines the probability of the variable taking each possible value. The sum of the probabilities of all possible outcomes must equal 1.
Continuous Random Variables
A continuous random variable is a variable that can take on any real number value. Examples of continuous random variables include the length of a person, the amount of time taken to get to work, or the temperature tomorrow.
The probability density function (PDF) of a continuous random variable defines the probability density at each point in the range of values the variable can take. The total probability under the PDF is equal to 1.
Probability Spaces and Random Variables
A probability space is a set of all possible outcomes of a random experiment. A random variable is a function that assigns a probability to each outcome in the probability space.
The probability space for a discrete random variable is a finite set of points, while the probability space for a continuous random variable is an infinite set of curves.
Examples
Discrete Random Variable: The number of successes in a sequence of independent coin tosses.
Continuous Random Variable: The height of a randomly selected adult