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What is a random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment.

What is a random variable?

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable might be discrete (meaning it has definite values) or continuous (meaning it has no specific values) (any value in a continuous range).

  1. Discrete Random Variable: A finite number of possible values for a discrete random variable. Each value of a discrete random variable has a probability between 0 and 1, and the sum of all probabilities equals 1.
  2. Continuous Random Variable: A continuous random variable takes on all of the values in a specific numerical interval. Continuous random variables are usually measurements. The amount of rainfall that will fall in June is an example of a continuous random variable.

Example of Random Variable:

Mean of Random Variable:

The mean of a discrete random variable is the weighted mean of the values. The formula is:

μx = x1*p1 + x2*p2 = Σ xipi.

The variance of Random Variable:

The formula for calculating the variance of a discrete random variable is:

σ2 = Σ(xi – μ)2f(x)

Note: This is also one of the AP Statistics formulas.
Σ (summation notation) means to “add everything up”,
μ = expected value,
xi = the value of the random variable,
f(x) is the probability (in function notation).

Why are random variables important?

A random variable is a method that provides unpredictable results by assigning unique numerical values to the outcomes of a random experiment. A probability distribution gives each conceivable value of a random variable a probability.

Owais Siddiqui
1 min read
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