Answer
a)The mean= $687.5$
The variance= $56.25$
b) The mean= $87.5$
The variance= $56.25$
we note that the boundaries a and b in the second question decreased by 600, this decreases the mean by 600 and has no effect on the variance
Work Step by Step
The mean of the uniform distribution is $\frac{b+a}{2}$
and the variance is $\frac{(b-a+1)^{2}-1}{12}$,
a) let a=675, b=700, then,
The mean= $\frac{700+675}{2}=\frac{1375}{2}=687.5$
The variance= $\frac{(700-675+1)^{2}-1}{12}=\frac{675}{12}=56.25$
b) let a=75, b=100, then,
The mean= $\frac{100+75}{2}=\frac{175}{2}=87.5$
The variance= $\frac{(100-75+1)^{2}-1}{12}=\frac{675}{12}=56.25$
we note that the boundaries a and b in the second question decreased by 600, this decreases the mean by 600 and has no effect on the variance
