Home Water Works says that in most homes, showers are the third-largest user of water after toilets and clothes washers. The average American shower water usage is 17.2 gallons with the average shower length being 8.2 minutes. The average flow rate is 2.1 gallons per minute.
Answer:
Step-by-step explanation:
A uniform distribution, "sometimes also known as a rectangular distribution, is a distribution that has constant probability".
We need to take in count that our random variable just take values between 0 and 1 since is uniform distribution (0,1). The maximum of the finite set of elements in (0,1) needs to be present in (0,1).
If we select a value we want this:
And we can express this like that:
for each possible i
We assume that the random variable are independent and
from the definition of an uniform random variable between 0 and 1. So we can find the cumulative distribution like this:
And then cumulative distribution would be expressed like this:
For each value we can find the dendity function like this:
So then we have the pdf defined, and given by:
and 0 for other case
And now we can find the expected value for the random variable X like this: