An Intermediate Course in Probability

On the definition of absorbed dose

“…For a full treatment see Gut (2009) or Chung (2001). A suitable probability space is defined in the following steps.…”

“…For a definition of expected value see Gut (2009). V x ( ) small is a volume of small mass surrounding the point x in the irradiated volume.…”

“…The domain of definition of a random variable is a sample space belonging to a probability space, designed to describe the real-world process we are considering (Gut, 2009), in this case the transfer of energy from ionizing radiation to matter. Therefore, to give a meaningful definition of specific energy imparted as a random variable it is necessary to define a suitable probability space.…”

“…Absorbed dose is then defined as the expected value of specific energy imparted. This implies that specific energy imparted is regarded as a random variable, which is a real-valued function defined on a probability space (Chung, 2001;Gut, 2009). The definition of specific energy imparted as a random variable, therefore, must specify a suitable probability space.…”

On reliability and robustness of scientometrics indicators based on stochastic models. An evidence-based opinion paper

“…Further information about attraction domains of distributions and weaker conditions of the central limit theorem can be found, e.g., in Rényi (1962), Hazewinkel (2002) or, more recently, Gut (2009).…”