Basics

Detector & statistics in a nutshell

1. Statistical data analysis in a nutshell
   
2. Probability
   
3. Probability Distributions
   Measurements deal with random processes: either the process under consideration is random (e.g. the number of decays observed in a bunch of unstable particle within a time interval T) or the measurement procedure contains random errors. The outcome of a measurement is hence considered as a random variable with a corresponding probability distribution.
   
   There are two types of probability distributions, namely for:
   
   a) DISCRETE RANDOM VARIABLES:
   e.g. the probability to observe N events in a counting experiment is given by a positive function P(N).
   
   b) CONTINUOUS RANDOM VARIABLES:
   For continuous random variables the probability to observe a certain result x is exactly zero:
   P(x)=0.
   Instead we are using here a probability density function (p.d.f.) f(x) which quantifies the probability to observe x lying in an interval [x,x+dx]: In case of more than one random variable we have to consider joint p.d.f.'s. E.g. in two dimensions, the probability for x to lie in an interval [x,x+dx] and for y to lie in an interval [y,y+dy] is given by If the two random variables x and y are independent then the joint p.d.f. factorizes: f(x,y)=g(x)h(y).
   
   
4. Cumulative Distributions
   
5. Expectation Values
   
6. Functions of random variables
   
7. Specific Probability Distributions
   
8. Parameter Estimation from Data
   
9. Statistical Tests
   
10. Basic detector concepts
    
11. Problems