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) = (2)/(10) = (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)=(1)/(10)`
c. The mean is given by:

`\mu=(a+b)/(2)=(0+10)/(2)=5`
d. The variance is given by:

`\sigma^2}=(1)/(12)(b-a)^(2)=(1)/(12)(10)^(2)=8.3333`
The standard deviation is:

`√(\sigma) = √(8.3333) =2.887`