# Advanced Math Find the final form of the median and range for uniform distribution (0,1) for order statistics.

Question
Upper Level Math
Find the final form of the median and range for uniform distribution (0,1) for order statistics.

2021-01-01
Step 1-Introduction
It is required to find the median and range for uniform distribution (0, 1).
Hence, the uniform distribution is U(0, 1) here and a = 0, b = 1.
The formulas for the median and range of the uniform distribution are as follows.
$$\displaystyle{M}{e}{d}{i}{a}{n}=\frac{{{a}+{b}}}{{2}}$$
Range=b-a
Step 2-Calculation
Here, a = 0 and b =1.
The median will be equal to:
$$\displaystyle{M}{e}{d}{i}{a}{n}=\frac{{{a}+{b}}}{{2}}$$
$$\displaystyle=\frac{{{0}+{1}}}{{2}}$$
=1/2 or 0.5
The range will be equal to:
Range = b -a
= 1 - 0
= 1
Hence, the median and range for uniform distribution (0, 1) is 0.5 and 1 respectively.

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