Uniform Distribution


Uniform probability distribution

Exhibit 33.14 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 33.14).

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.


What they SHOULD TEACH at Business Schools

What they SHOULD TEACH at Business Schools


Is marketing education fluffy too?


Experiential Learning via Simulators | Best Way to Train Marketers

Experiential Learning via Simulators | Best Way to Train Marketers


Marketing simulators impart much needed combat experiences, equipping practitioners with the skills to succeed in the consumer market battleground. They combine theory with practice, linking the classroom with the consumer marketplace.