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Contents Gamma Distribution Gamma function Gamma distribution Chi-square distribution F distribution Gamma Distribution Since the probability is the ratio of the target cases to the total number of cases, it is important to calculate the total number of cases in calculating the probability. For discrete variables, the total number of cases is calculated using factorial. In the case of continuous variables, the factorial cannot be calculated directly because random variables are not countable. Instead, an integral expression corresponding to factorial is used, which can be replaced with gamma function . Therefore, the gamma distribution based on the gamma function is a distribution related to the exponential distribution and the normal distribution and is used in various fields. Gamma function The gamma function is expressed as Γ(x) and has the form of a factorial function in the realm of natural numbers, and is defined as Equation 1 for discrete and continuous va...

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...