1. 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.

2. 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].

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

4. 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.

5. Continuous Probability Distribution
Uniform distribution

6. 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.

7. Continuous Probability Distribution
Mean and variance of a uniform distribution

8. Continuous Probability Distribution
Variance

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

10. Continuous Probability Distribution
Example 1:

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

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

13. 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:

14. Continuous Probability Distribution
Solution:

15. 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?

16. Continuous Probability Distribution
Solution: