Continuous random variable

Unlike a discrete random variable, a continuous, random variable (CRV) can take on any value within a certain range - not just a set number. This means that instead of counting the number of outcomes, we measure the probability of an outcome occurring within a specific interval.

The probability of getting exactly any specific value is actually zero for a CRV, because there are infinitely many possible values. either side of it.

flashcards

QuestionAnswer
What is a continuous random variable?It can take any value within a range, not just a set number of values; probability is measured over intervals.
What is the probability of a continuous random variable taking exactly one specific value?It is zero, because there are infinitely many possible values.
What is the key difference between a discrete random variable and a continuous random variable?A discrete variable takes a set number of outcomes; a continuous variable takes any value in a range, so probability is measured over intervals.
Why can’t you count the number of outcomes for a continuous random variable the way you do for a discrete one?Because a continuous variable can take infinitely many values within a range, so you measure probability over intervals instead of counting outcomes.