Random Variable

Sure, here’s a definition of a random variable:

Random variable: A function that assigns a numerical value to each outcome of a random experiment.

Formal definition:A random variable is a function from the sample space S of an experiment to the set of real numbers R. A random variable is represented by a letter like X. For every subset A of S, the probability of X falling into A is defined by P(A) = P(X belongs to A).

Key points:

• Random variable: A function that assigns a numerical value to each outcome of a random experiment.
• Sample space: The set of all possible outcomes of a random experiment.
• Real numbers: The set of all numbers.
• Probability: The probability of a random variable falling into a given subset of its sample space.

Examples:

• Random variable X: The number of heads obtained in a coin toss experiment.
• Random variable Y: The number of defective products in a batch of 100 products.
• Random variable Z: The waiting time for a bus at a bus stop.

Additional notes:

• Random variables are used to quantify the uncertain outcomes of an experiment.
• The probability of a random variable falling into a given set can be calculated using the probability mass function (for discrete variables) or the probability density function (for continuous variables).
• Random variables can be used to perform statistical analyses and make predictions about the outcome of an experiment.

Here are some resources that you may find helpful:

• Khan Academy: Random Variables: Math/Statistics/Probability/Random Variables
• Stattrek: Random Variables: Probability/Random Variables
• Cambridge University: Random Variables: Probability/Random Variables

Please let me know if you have any further questions about random variables.