The triangular distribution is commonly used in simulations, risk analysis, and probabilistic modeling. It is defined by a lower limit, upper limit, and a mode, representing the most likely value. Use this calculator to compute probabilities and visualize the distribution.

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**Mean:**

**Median:**

**Variance:**

## Understanding the Triangular Distribution

The **Triangular Distribution** is a continuous probability distribution defined by a lower limit, an upper limit, and a mode, which represents the most likely value. It is commonly used in simulations and risk analysis.

### Key Components of the Triangular Distribution

**Lower Limit (a):**The minimum possible value.**Upper Limit (b):**The maximum possible value.**Mode (c):**The most likely value in the distribution.

### Formula for Triangular Distribution

The probability density function (PDF) for the triangular distribution is given by:

### Step-by-Step Example

Let's assume the lower limit is \(a = 1\), the upper limit is \(b = 10\), and the mode is \(c = 5\). If we want to find the probability for \(x = 4\), we apply the formula above.

#### Mean, Median, and Variance

**Mean (μ):**\( \frac{a + b + c}{3} \)**Median:**If \( c \leq \frac{a + b}{2} \), the median is \( a + \sqrt{(b-a)(c-a)/2} \). Otherwise, the median is \( b - \sqrt{(b-a)(b-c)/2} \).**Variance (σ²):**\( \frac{a^2 + b^2 + c^2 - ab - ac - bc}{18} \)