Uniform Distribution

Uniform probability distribution

Exhibit 33.15 Uniform probability distribution.

Uniform distribution, or rectangular distribution, is a distribution that has constant probability over a fixed range. A random variable, X, is uniform on [a,b] if X is equally likely to take any value in the range from a to b (Exhibit 33.15).

Notation: [a, b] means continuous values from a to b.

$$X∼U[a,b]$$ $$f(t)=\begin{cases}\frac{1}{b-a}, \,\,if \,\,a \, \le t \le b \\ \\0 \,otherwise \end{cases}$$

The cumulative distribution function (cdf):

$$F(t)=\begin{cases}0 \,\,if \,\,t< a \\ \\ \frac{t-a}{b-a} \,\,if \,\,a \le t \le b \\ \\ 1 \,\,if \,\,t>b \end{cases}$$ $$E(X)= \frac{b-a}{2}, \,Var(X)=\frac{b-a}{12}$$

Previous     Next

Use the Search Bar to find content on MarketingMind.

Marketing Analytics Workshop

Marketing Analytics Workshop

In an analytics-driven business environment, this analytics-centred consumer marketing workshop is tailored to the needs of consumer analysts, marketing researchers, brand managers, category managers and seasoned marketing and retailing professionals.

Digital Marketing Workshop

Digital Marketing Workshop

Unlock the Power of Digital Marketing: Join us for an immersive online experience designed to empower you with the skills and knowledge needed to excel in the dynamic world of digital marketing. In just three days, you will transform into a proficient digital marketer, equipped to craft and implement successful online strategies.