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Elodia [21]
3 years ago
9

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?
Mathematics
1 answer:
IgorC [24]3 years ago
5 0
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


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