Basics

Detector & statistics in a nutshell

1. Statistical data analysis in a nutshell
   
2. Probability
   
3. Probability Distributions
   
4. Cumulative Distributions
   
5. Expectation Values
   The EXPECTATION VALUE E[x] (also called MEAN VALUE) of a random variable x with corresponding p.d.f. f(x) is defined as More generally, the N-TH ALGEBRAIC MOMENT of x is defined as the following expectation value The second central moment, the VARIANCE, measures the spread of the random variable x around its mean value. The square root of the variance is called the STANDARD DEVIATION.
   For two random variables the generalization of the variance is the COVARIANCE The covariance is a measure of the CORRELATION between two random variables.
   
   If two variables are independent then they are also uncorrelated. However, two variables may be uncorrelated but are not independent.
   
   With these definitions in hand we can also give the error propagation formula. If y is a function of random variables x=(x₁,x₂) then mean and variance of y can be expressed by the mean values and variances in x as follows:
   
   
6. Functions of random variables
   
7. Specific Probability Distributions
   
8. Parameter Estimation from Data
   
9. Statistical Tests
   
10. Basic detector concepts
    
11. Problems