Uniform Distribution
Tags: #Math #StatisticsEquation
$$X \sim U(a,b) \\ f(x)=\frac{1}{b-a} \text{for} a \le x \le b \text{else} 0 \\ F(x)=\frac{x-a}{b-a} \text{for} a \le x \le b, 1 \text{for} x > b, 0 \text{for} x < a$$Latex Code
X \sim U(a,b) \\
f(x)=\frac{1}{b-a} \text{for} a \le x \le b \text{else} 0 \\
F(x)=\frac{x-a}{b-a} \text{for} a \le x \le b, 1 \text{for} x > b, 0 \text{for} x < a
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Introduction
Equation
$$X \sim U(a,b)$$ $$f(x)=\frac{1}{b-a} \text{for} a \le x \le b \text{else} 0$$ $$F(x)=\frac{x-a}{b-a} \text{for} a \le x \le b, 1 \text{for} x > b, 0 \text{for} x < a $$
Latex Code
X \sim U(a,b) \\
f(x)=\frac{1}{b-a} \text{for} a \le x \le b \text{else} 0 \\
F(x)=\frac{x-a}{b-a} \text{for} a \le x \le b, 1 \text{for} x > b, 0 \text{for} x < a
Explanation
Latex code for the Uniform Distribution.
- Lower Bound parameter: $$a$$
- Upper Bound parameter: $$b$$
- PDF for Uniform Distribution: $$f(x)=\frac{1}{b-a} \text{for} a \le x \le b \text{else} 0$$
- CDF for Uniform Distribution: $$F(x)=\frac{x-a}{b-a} \text{for} a \le x \le b, 1 \text{for} x > b, 0 \text{for} x < a$$
- Mean for Uniform Distribution: $$\frac{a+b}{2}$$
- Variance for Uniform Distribution: $$\frac{(b-a)^{2}}{12}$$
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