Basics

Detector & statistics in a nutshell

  1. Statistical data analysis in a nutshell
  2. Basic detector concepts
  3. Problems
    1. Prove that the mean value of the Poissonian distribution is given by its parameter μ.
    2. Calculate the mean value and the variance for the uniform distribution.
    3. Prove that y=F(x) is a random variable which is uniformly distributed between 0 and 1 (g(y)=1 for y in [0,1]; g(y)=0 otherwise) if F(x) is the cumulative function of the random variable x with p.d.f. f(x).
    4. Suppose we have measured n decay times of a certain type of particles, t1, ..., tn. Calculate the Maximum Likelihood estimator for the lifetime τ.