Answer:
![E(X)= n \int_{0}^1 x^n dx = n [\frac{1}{n+1}- \frac{0}{n+1}]=\frac{n}{n+1}](https://tex.z-dn.net/?f=E%28X%29%3D%20n%20%5Cint_%7B0%7D%5E1%20x%5En%20dx%20%3D%20n%20%5B%5Cfrac%7B1%7D%7Bn%2B1%7D-%20%5Cfrac%7B0%7D%7Bn%2B1%7D%5D%3D%5Cfrac%7Bn%7D%7Bn%2B1%7D)
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:
Answer:
(2x -4) (Find your answer) then add your answers and divide it by 180
Multiply 12 by 4%, or 4/100, and 4/100 simplifies to 1/25. 12/1 x 1/25 = (12 x 1)/(1 x 25) = 12/25, which equals 0.48. So, the smallest frog is 0.48 inches long, but can be rounded to 0.5 inches long.
Divide the second price by the second pounds. 9.95 / 5 = 1.99
So for every pound you get you pay 1.99 dollars. The second deal is better.
-3x-8=10
First add 8 to both sides
-3x=18
Then divide both sides by -3
x=-6
