The characteristic function approach is particularly useful in analysis of linear combinations of independent random variables : a classical proof of the Central Limit Theorem uses characteristic functions and L�vy's continuity theorem.
32.
A converse is Raikov's theorem, which says that if the sum of two independent random variables is Poisson-distributed, then so is each of those two independent random variables.
33.
A converse is Raikov's theorem, which says that if the sum of two independent random variables is Poisson-distributed, then so is each of those two independent random variables.
34.
The difference between 0.85185 . . . and 0.85558 . . . seems remarkably small when it is considered that the number of independent random variables that were added was only three.
35.
Observe that, even if \ mu is close to 1, h ( x _ i ) are no longer independent random variables, which is often a problem in the analysis of randomized algorithms.
36.
*PM : moment generating function of the sum of independent random variables, id = 9628 new !-- WP guess : moment generating function of the sum of independent random variables-- Status:
37.
*PM : moment generating function of the sum of independent random variables, id = 9628 new !-- WP guess : moment generating function of the sum of independent random variables-- Status:
38.
To see how this implies the preservation of log-convexity by independent sums, suppose that " X " and " Y " are independent random variables with log-concave distribution.
39.
Given a set of bad events \ mathcal { A } we wish to avoid that is determined by a collection of mutually independent random variables \ mathcal { P }, the algorithm proceeds as follows:
40.
:It also follows that the probability generating function of the difference of two independent random variables " S " = " X " 1 & minus; " X " 2 is
