CIE A Level Maths: Probability & Statistics 2復(fù)習(xí)筆記2.3.3 Continuous Uniform Distribution
Continuous Uniform Distribution
What is meant by the continuous uniform distribution?
- This is a special case of a probability density function for a continuous random variable
- The?normal?distribution?is another special case covered in S1
- The?uniform, or?rectangular,?distribution?is a p.d.f. that is?constant?and?non-zero?over a range of values but zero everywhere else
How do I find probabilities for a continuous uniform distribution?
- Sketch?the graph of y= f(x)
- Probabilities are the?area?under?the?graph, all such?areas?will now be?rectangles
- Finding the area of a rectangle is likely to be easier than integration!
- The?symmetrical?properties of rectangles may also be used to find probabilities
How do I find the mean, median, mode and variance of a continuous uniform distribution?
-
You may be asked to use this to prove the result- The?standard?deviation?is the?square?root?of the?variance
Worked Example
Exam Tip
- A?sketch?of the graph of a uniform distribution is quick and will highlight the?symmetry?in a uniform distribution
- Use?areas?of?rectangles?to find?probabilities?rather than integrating
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