2024年5月13日发(作者：睢浩气)
S.-legeStudentMathematicsContests2021
ProbabilityandStatistics
Solveeveryproblem.
PartI:Probability
ethatasequence
{
X
n
}
ofreal-valuedrandomvariablesconvergestoXindistribution
andtherearepositiveconstantsrandCsuchthatE|X
n
|
r
≤at
n→∞
limE|X
n
|
s
=E|X|
s
forall0 (x,y)bethe(one-step)transitionfunctionofaMarkovchainonadiscretestatespaceS andp n (x,y)atforanypositiveintegersLandNandanytwostates xandywehave N+LN
2024年5月13日发(作者：睢浩气)
S.-legeStudentMathematicsContests2021
ProbabilityandStatistics
Solveeveryproblem.
PartI:Probability
ethatasequence
{
X
n
}
ofreal-valuedrandomvariablesconvergestoXindistribution
andtherearepositiveconstantsrandCsuchthatE|X
n
|
r
≤at
n→∞
limE|X
n
|
s
=E|X|
s
forall0 (x,y)bethe(one-step)transitionfunctionofaMarkovchainonadiscretestatespaceS andp n (x,y)atforanypositiveintegersLandNandanytwostates xandywehave N+LN