The mean of the uniform distribution of X is the average of the distribution
The mean and standard deviation of X are 18 and 9.24, respectively
The uniform distribution of X is given as:
X∼U(3,34)
This means that:
a = 3 and b = 34
The mean is calculated as:
[tex]\bar x = \frac{a + b}{2}[/tex]
So, we have:
[tex]\bar x = \frac{2 + 34}{2}[/tex]
[tex]\bar x = \frac{36}{2}[/tex]
Evaluate
[tex]\bar x = 18[/tex]
This is calculated as:
[tex]\sigma = \sqrt{\frac{(b - a)^2}{12}}[/tex]
Substitute known values
[tex]\sigma = \sqrt{\frac{(34 - 2)^2}{12}}[/tex]
Evaluate the exponent
[tex]\sigma = \sqrt{\frac{1024}{12}}[/tex]
Divide
[tex]\sigma = \sqrt{85.33}[/tex]
Evaluate the root
[tex]\sigma = 9.24[/tex]
Hence, the mean and standard deviation of X are 18 and 9.24, respectively
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