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　　2.Uniform Distribution:

　　\begin{equation}
　　f(x|a, b) = \begin{cases}
　　\frac{1}{b-a} & \text{for } a \leq x \leq b \\
　　0 & \text{otherwise}
　　\end{cases}
　　\end{equation}

　　The uniform distribution has constant probability density between two points a and b. It is often used to model situations where each outcome within an interval is equally likely.\\

　　3. Exponential Distribution:
　　\begin{equation}
　　f(x|\lambda) = \begin{cases}
　　\lambda e^{-\lambda x} & \text{for } x \geq 0 \\
　　0 & \text{otherwise}
　　\end{cases}
　　\end{equation}

　　The exponential distribution describes the time between events in a Poisson process, where events occur continuously and independently at a constant rate $\lambda$.\\

　　4. Poisson Distribution:

　　\begin{equation}
　　P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} \quad \text{for } k = 0, 1, 2, \ldots
　　\end{equation}

　　The Poisson distribution models the number of events occurring in a fixed interval of time or space, given a constant average rate of occurrence $\lambda$.\\

　　5. Binomial Distribution:

　　\begin{equation}
　　P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \quad \text{for } k = 0, 1, 2, \ldots, n
　　\end{equation}

　　The binomial distribution describes the number of successes in a fixed number n of independent Bernoulli trials, where each trial has probability of success p.\\

　　These distributions are fundamental in statistics and have various applications in modeling real-world phenomena. They are characterized by their PDFs, which specify the probabilities of different outcomes.Table 1 presents the parameter estimates for these common distributions.\\