CIE A Level Maths: Probability & Statistics 2复习笔记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?
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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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