SaiBook.us Statistics

Lesson

Title: Uniform distribution

Grade: 9-a Lesson: S4-L8

Explanation: Hello students, let us learn a new topic in statistics today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Uniform distribution:

The uniform distribution is rectangular in shape, implying that any value in the distribution has an equal chance of occurring.

A uniform distribution is used in any case where every event in a sample space is equally likely.

A random variable X is said to have a continuous Uniform distribution over the interval (a, b) if its probability density function

Notation: X ∼ U(a,b)

$1$

Explanation:

Characteristics of uniform Distribution:

a and b are the parameters of the Uniform distribution and we write X ~ U (a, b)
The distribution is also known as Rectangular distribution, as the curve
y = f(x) describes a rectangle over the x-axis and between ordinates at x = a and x= b.
f(X) ~ U (-a, a) then its p.d.f. is

f(X) = \$1/(2a)\$ where -a<x<a

Constants of uniform distribution X ∼ U(a,b) :

Calculating the height of the rectangle:

The total area of the rectangle equals 1, the total probability of the variable X.

area of rectangle = base • height = 1

(b – a) • f(x) = 1

\$f(x) = 1/(b – a)\$ = height of the rectangle