uuuThis deserves its own textbook.
The single most important thing to know about the normal distribution is that it is like the mother distribution. It describes so many real world phenomenon, due to the fact that it arises as the sum of many random variables.
And when you think about it, most phenomenon - human height, the number of trains passing through a station - are the result of a sum of many random variables, and thus asymptotically normal.
Note how relaxed these assumptions are:
- they don’t even need to be normal
- they don’t need to be normal themselves
- they don’t even really need to be independent
Law of large numbers
Central limit theorem
Q1) What is the bell-shaped distribution used to model many natural phenomena?
Normal Distribution
(we will come back to this)
Q2) How can we model a random variable that is equally likely to take on any value in a given range?
Uniform
The uniform distribution models a random variable that is equally likely to take on any value within a given range. Its parameters are:
- ( a ) and ( b ) which are the minimum and maximum values, respectively.
- Expected value (mean) = ( \frac{a+b}{2} )
- Variance = ( \frac{(b-a)^2}{12} )