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Contents Probability Density Function(PDF) Continuous Possibility Distribution If the probability of randomly selecting a number in a certain interval [a, b] is the same, the number becomes a random variable, and since the number of the interval is infinite, a single point cannot be specified. In other words, the probability at a particular point in a continuous variable cannot be defined. Instead, if intervals with equal probabilities are grouped, the probability of selecting a group can be defined as the length of that selected portion over the length of the entire interval. This relationship can be expressed as Equation 1. $$\begin{align}\tag{1} P(X \in [a, b])&=1\\ P(X \in [x_1, x_2])& \varpropto (x_2-x_1)\\&= \frac{x_2-x_1}{b-a}\\ a\le x_1 \le x_2\le b \end{align}$$ Based on the above expression, the cumulative distribution function (CDF) for the random variable X is written as Equation 2. $$\begin{align}\tag{2} F(X)=\begin{cases} 0 & \quad \text{fo...