Question

Learning the basics 6.23 suppose you select one value from a uniform distribution with a=0and b=10.what is the probability that the value will be
a. between 5 and 7?
b. between 2 and 3?
c. what is the mean?
d. what is the standard deviation?

Answer 1

The area under the graph of the continuous uniform distribution is 1.
a. The probability that the value will be between 5 and 7 is the area between 5 and 7.
$P(5 \ \textless \ x \ \textless \ 7) = \frac{2}{10} = \frac{1}{5}$
b. The probability that the value will be between 2 and 3 is the are between 2 and 3.
$P(2 \ \textless \ x \ \textless \ 3)=\frac{1}{10}$ 
c. The mean is given by:
$\mu=\frac{a+b}{2}=\frac{0+10}{2}=5$
d. The variance is given by:
$\sigma^2}=\frac{1}{12}(b-a)^{2}=\frac{1}{12}(10)^{2}=8.3333$
The standard deviation is:
$\sqrt{\sigma} = \sqrt{8.3333} =2.887$