Summary: Math 501. 6­th Homework. Due Friday, November 30, 2007.
Homework on "Common discrete and continuous distributions".
Name: ...............................................................................................................................................
1. Let {an}
n=1 be a sequence of real numbers. Suppose that there exists R > 0 such
that
n=0 |an|Rn
< . Then,
(i) For each |x| R, f(x) =
n=0 anxn
exist.
(ii) For each |x| < R, g(x) =
n=1 annxn-1
exist.
(iii) For each |x| < R, f (x) = g(x).
(iv) For each n 0, an = f(n)(0)
n!
2. Let 0 < p 1. Let Y be a r.v. Suppose that:
(i) P[Y N] = 1.
(ii) For each k, n N,

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

Collections: Mathematics