s******n
发帖数: 110 | 1 If Y is a discrete random variable that assigns positive probabilities to
only the positive integers, show that
E(Y) = Summation of (i=1 to infinite) of P(Y>=k) |
f*********y
发帖数: 376 | 2 it is obvious...and the subscript should be k not i
【在 s******n 的大作中提到】
: If Y is a discrete random variable that assigns positive probabilities to
: only the positive integers, show that
: E(Y) = Summation of (i=1 to infinite) of P(Y>=k)
|
h***i
发帖数: 3844 | 3 Sum (i=1 to infinite) of P(Y>=i)
=Sum (i=1 to infinite)Sum (k=i to infinite)P(Y=k)
=Sum (k=1 to infinite)Sum (i=1 to k)P(Y=k)
=Sum (k=1 to infinite)kP(Y=k)
=E(Y)
【在 s******n 的大作中提到】
: If Y is a discrete random variable that assigns positive probabilities to
: only the positive integers, show that
: E(Y) = Summation of (i=1 to infinite) of P(Y>=k)
|
s******n
发帖数: 110 | 4 Thanks to you, brother!! |
s******h
发帖数: 539 | 5 The general result is, for any non-negative measurable function g,
E(g(X)) = \int_{[0, \infty)} Pr(g(X) >=t) dm(t), where m is the Lebesgue
measure. It can be quite useful sometimes.
【在 s******n 的大作中提到】
: Thanks to you, brother!!
|
