Given a continuous random variable, the probability density function describes the relative probability that value of the random variable would be equal to that value. For example given the probability density function and the random variable we can say that the relative probability that is between and is equal to .
Rules
For any probability density function , the following must be true
Rationale
Zero
asks the question what is the probability that the random variable is a single number , this is because the random variable is continuous, which means that there are infinite values between any, two numbers, this means that your chance of picking just one number from an infinite amount is always 0.
Total Probability
asks what the chance that the random variable is a number, which must always be true mean it must equal 1.
Positive or Zero
must always be true because you can not have a negative probability for a random variable to take on a given value.