Explain the procedure of assigning probability in a continuous world of probability theory.

Assigning probabilities in a continuous world of probability theory involves dealing with random variables that can take on an infinite number of values within a given range. Unlike discrete probability, where we can assign probabilities to specific events or outcomes, continuous probability deals with probability density functions (PDFs) and cumulative distribution functions (CDFs) over a continuous range of values. Here's a step-by-step procedure for assigning probabilities in a continuous probability context:

1. Define the Random Variable (RV):
   - Start by defining the random variable that represents the quantity or measurement you are interested in. For example, if you are modeling the height of individuals, the random variable might be denoted as X.

2. Identify the Probability Density Function (PDF):
   - In continuous probability theory, we use a probability density function (PDF) to describe the probability distribution of the random variable X. The PDF is denoted as and provides the probability density at each point within the range of the variable.
   - The PDF must satisfy the following properties:
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