Probabilistic analysis and Random algorithm

(1) Cost Model and Running Time Model are different
(2) The Technique which is used to analyze Cost Model and Running Time Model is the same.
(3) It is to count the number of operation execution in the routine algorithm
(4) Probabilistic analysis is one of a technique which fits in the use case where there is a input distribution. However, if we can not describe a reasonable input distribution, we can not use probabilistic analysis.
(5) In many case, we only can know a little bit about the distribution of the input but can not model the knowledge of the input distribution.
(6) Random algorithm is controlled not only by input distribution but also random-number generator
so that we can have a level of control which I do not need to guess and make assumption that input
comes in with random order instead we choose input randomly to ensure input is definitely random.
We used to call a pseudorandom number generator --- deterministic algorithm returning random number
(7) Probabilistic analysis impose a distribution rather than assuming a distribution of inputs to
the development of the randomized algorithm
(8)