Convergence of expectation of random variables Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Sequence of independent random variables: Convergence, martingales, uniform integrabilityConvergence of random variableConvergence equivalent random sequencesconvergence of expectation sum of infinite random variablesDifference of two random variables and convergenceConvergence of expectations of random variablesConvergence of exponentially-distributed random variablesConvergence of conditional expectation of multiplication of two sequencesConvergence in probability of sum of bounded random variables implies finite expectationConvergence of random variable Poisson distribution
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Convergence of expectation of random variables
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Sequence of independent random variables: Convergence, martingales, uniform integrabilityConvergence of random variableConvergence equivalent random sequencesconvergence of expectation sum of infinite random variablesDifference of two random variables and convergenceConvergence of expectations of random variablesConvergence of exponentially-distributed random variablesConvergence of conditional expectation of multiplication of two sequencesConvergence in probability of sum of bounded random variables implies finite expectationConvergence of random variable Poisson distribution
$begingroup$
$X$ is a non negative random variable . Define :
$ Y_n = sum_k=1^inftyfrack2^nmathbbI(frack-12^n le X < frack2^n)$
Does $ mathbbE[Y_n] rightarrow mathbbE[X] $ as $n rightarrow infty$ ?
I have a hunch that $mathbbE[Y_n]$ might be decreasing , but I am unable to prove it rigorously .
probability-theory expected-value
asked Mar 27 at 3:42
JohnJohn
363113
$endgroup$
add a comment |
$begingroup$
$X$ is a non negative random variable . Define :
$ Y_n = sum_k=1^inftyfrack2^nmathbbI(frack-12^n le X < frack2^n)$
Does $ mathbbE[Y_n] rightarrow mathbbE[X] $ as $n rightarrow infty$ ?
I have a hunch that $mathbbE[Y_n]$ might be decreasing , but I am unable to prove it rigorously .
probability-theory expected-value
asked Mar 27 at 3:42
JohnJohn
363113
$endgroup$
add a comment |
$begingroup$
$X$ is a non negative random variable . Define :
$ Y_n = sum_k=1^inftyfrack2^nmathbbI(frack-12^n le X < frack2^n)$
Does $ mathbbE[Y_n] rightarrow mathbbE[X] $ as $n rightarrow infty$ ?
I have a hunch that $mathbbE[Y_n]$ might be decreasing , but I am unable to prove it rigorously .
probability-theory expected-value
asked Mar 27 at 3:42
JohnJohn
363113
$endgroup$
$X$ is a non negative random variable . Define :
$ Y_n = sum_k=1^inftyfrack2^nmathbbI(frack-12^n le X < frack2^n)$
Does $ mathbbE[Y_n] rightarrow mathbbE[X] $ as $n rightarrow infty$ ?
I have a hunch that $mathbbE[Y_n]$ might be decreasing , but I am unable to prove it rigorously .
probability-theory expected-value
probability-theory expected-value
asked Mar 27 at 3:42
JohnJohn
363113
asked Mar 27 at 3:42
JohnJohn
363113
asked Mar 27 at 3:42
JohnJohn
363113
asked Mar 27 at 3:42
JohnJohn
363113
asked Mar 27 at 3:42
JohnJohn
363113
363113
add a comment |
add a comment |
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