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Prove for a random variable $X$,$(E|X|^2)^2le E|X|E|X|^3$
a question about random variableWhen is there in a probability space no null sets?Computing Char. Function of a Random VariableInequality for inverse random variableConvergence in probability of exponentially distributed random variableDo we have $ int_A chi_B mu = mu(A) $ in a probability space?Chebyshev inequality for some random variableHow to show a binomial random variable dominates another binomial random variable with a smaller success value?Upper bound for quantile a random variableAlmost sure convergence of product of two random variable
$begingroup$
More general, for $alphain[0,2)$, is $(E|X|^2)^2le E|X|^2-alphaE|X|^2+alpha$ always true?
I don't have any idea to deal with such inequality concerning three expectations. Can someone give an idea on proving it? Thank you!
probability-theory
asked Mar 16 at 10:19
zbh2047zbh2047
639
$endgroup$
add a comment |
$begingroup$
More general, for $alphain[0,2)$, is $(E|X|^2)^2le E|X|^2-alphaE|X|^2+alpha$ always true?
I don't have any idea to deal with such inequality concerning three expectations. Can someone give an idea on proving it? Thank you!
probability-theory
asked Mar 16 at 10:19
zbh2047zbh2047
639
$endgroup$
4
$begingroup$
Apply Cauchy's inequality with $f=|X|^(2-a)/2$, $g=|X|^(2+a)/2$.
$endgroup$
– user647486
Mar 16 at 11:33
$begingroup$
Thank you so much!
$endgroup$
– zbh2047
Mar 16 at 13:03
add a comment |
$begingroup$
More general, for $alphain[0,2)$, is $(E|X|^2)^2le E|X|^2-alphaE|X|^2+alpha$ always true?
I don't have any idea to deal with such inequality concerning three expectations. Can someone give an idea on proving it? Thank you!
probability-theory
asked Mar 16 at 10:19
zbh2047zbh2047
639
$endgroup$
More general, for $alphain[0,2)$, is $(E|X|^2)^2le E|X|^2-alphaE|X|^2+alpha$ always true?
I don't have any idea to deal with such inequality concerning three expectations. Can someone give an idea on proving it? Thank you!
probability-theory
probability-theory
asked Mar 16 at 10:19
zbh2047zbh2047
639
asked Mar 16 at 10:19
zbh2047zbh2047
639
edited Mar 16 at 10:24
zbh2047
asked Mar 16 at 10:19
zbh2047zbh2047
639
asked Mar 16 at 10:19
zbh2047zbh2047
639
asked Mar 16 at 10:19
zbh2047zbh2047
639
639
4
$begingroup$
Apply Cauchy's inequality with $f=|X|^(2-a)/2$, $g=|X|^(2+a)/2$.
$endgroup$
– user647486
Mar 16 at 11:33
$begingroup$
Thank you so much!
$endgroup$
– zbh2047
Mar 16 at 13:03
add a comment |
4
$begingroup$
Apply Cauchy's inequality with $f=|X|^(2-a)/2$, $g=|X|^(2+a)/2$.
$endgroup$
– user647486
Mar 16 at 11:33
$begingroup$
Thank you so much!
$endgroup$
– zbh2047
Mar 16 at 13:03
4
4
$begingroup$
Apply Cauchy's inequality with $f=|X|^(2-a)/2$, $g=|X|^(2+a)/2$.
$endgroup$
– user647486
Mar 16 at 11:33
$begingroup$
Apply Cauchy's inequality with $f=|X|^(2-a)/2$, $g=|X|^(2+a)/2$.
$endgroup$
– user647486
Mar 16 at 11:33
$begingroup$
Thank you so much!
$endgroup$
– zbh2047
Mar 16 at 13:03
$begingroup$
Thank you so much!
$endgroup$
– zbh2047
Mar 16 at 13:03
add a comment |
0
active
oldest
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4
$begingroup$
Apply Cauchy's inequality with $f=|X|^(2-a)/2$, $g=|X|^(2+a)/2$.
$endgroup$
– user647486
Mar 16 at 11:33
$begingroup$
Thank you so much!
$endgroup$
– zbh2047
Mar 16 at 13:03