Random variable
A random variable is a number that depends on chance. Its probability distribution lists every possible value and how likely each one is. The probabilities must add up to 1.
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Analogy
A game show wheel: the wheel is the chance process, and the number it lands on is the random variable.
Example
X = number of headsP(X=0) = 0.25 (TT)P(X=1) = 0.50 (HT, TH)P(X=2) = 0.25 (HH)Total = 1.00
In practice
Counts of customers, the sum of two dice and waiting times are all random variables.
Practice
Flashcards
- What must probabilities of a distribution add up to?Exactly 1.
Questions people ask
What is the difference between a random variable and a normal variable?
In algebra a variable stands for one unknown value. A random variable takes different values on different occasions, each with a set probability. Before you flip the coin you do not know the count of heads, but you know how likely each count is.
What is the difference between a discrete and a continuous random variable?
A discrete random variable takes countable values, such as 0, 1, 2 goals. A continuous one can take any value in a range, such as a height or a waiting time. Discrete variables use probabilities for each value. Continuous ones use areas under a curve.