To find the Mean, Expected Value, Variance & Standard Deviation
f(x) = 1/(b-a) If X is uniformly distributed on [a,b]
f(x) = 1/(b-a) or you could say for a<x<b
Mean or Expected Value of a Uniform Distribution (when X is a Continous Random Variable)
E(X) = (a + b)/ 2
E(X) = µ = Mean of a Normal Distrubution
Variance
Var(X) = (b-a)2 /12
Standard Deviation
σ(X) = (b−a)/120.5
example: f(x) = 1/2 over an interval [1 , 3 ]
Mean ................. E(X) = (a + b)/ 2 = (3+1)/2 = 4/2 = 2
Variance ............. Var(X) = (b-a)2 /12 = (3-1)2 /12 = 4/12 = 1/3
Standard Deviation ... σ(X) = (b−a)/120.5 = (3-1)/120.5 = 2/(3.464102) = .577321
Where does the formula get the 12? https://www.youtube.com/watch?v=ieFxnBU8stM
Note: Formulas found on https://www.zweigmedia.com/RealWorld/cprob/cprob3.html
and http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm