Continuous Probability Distribution Introduction: A continuous random variable has infinity many values, and those values are often associated with measurements on a continuous scale with no gaps.

Continuous Probability Distribution Continuous uniform distribution: It is the simplest continuous distribution above all the statistics continuous distribution. This distribution is characterized by a density functions flat and thus the probability is uniform in a closed interval [A,B].

Continuous Probability Distribution The density function of a uniform continuous distribution X on interval [A,B] is:

Continuous Probability Distribution The density function forms a rectangle with base [B-A] and constant height so that the uniform distribution is often called the rectangular distribution.

Continuous Probability Distribution Uniform distribution

Continuous Probability Distribution Uses of uniform distribution: In risk analysis. The position of a particular air molecule in a room. The point on a car tire where the next puncture will occur. The length of time that some one needs to wait for a service.

Continuous Probability Distribution Mean and variance of a uniform distribution

Continuous Probability Distribution Variance

Continuous Probability Distribution Example 1: The continuous random variable X has a probability distribution function (f(x)) as the figure bellow

Continuous Probability Distribution Example 1:

Continuous Probability Distribution Find: 1. The value of k. 3. E(X)

Continuous Probability Distribution Solution: The area under the curve must be equal 1. Then

Continuous Probability Distribution Example 2: The current in (mA) measured in a piece of copper wire is known to follow a uniform distribution over the interval [0,25]. Write down the formula for probability density function f(X) of random variable X representing the current. Calculate mean and variance of distribution. Solution:

Continuous Probability Distribution Solution:

Continuous Probability Distribution Example 3: Suppose that a large conference room at a certain company can be reserved for no more than 4 hours. Both long and short conference occurs quite often. In fact it can be assumed that the length X of a conference has a uniform distribution on the interval [0,4] What is the probability density function? What is the probability that any given conference at least 3 hours? Calculate mean?

Continuous Probability Distribution Solution: