/sci/ - Science & Math

[Anonymous No.8438175]

Can this be simplified?

[math]E \left[ E[Y^2 \mid| X] - (E[Y \mid X])^2 \right] [/math]

Does it simplify to [math] E[Y \mid X ] [/math]

[Anonymous No.8438176]

fucked that up a bit.. take 2
[math] E \left[ E[Y^2 \mid X] - ( E[Y \mid X])^2 \right]

[Anonymous No.8438178]

[math] E \left[ E[Y^2 \mid X] - ( E[Y \mid X])^2 \right] [\math]

[Anonymous No.8438180]

last try before i kms

[math] E \left[ E[Y^2 \mid X] - ( E[Y \mid X])^2 \right] [/math]

[Anonymous No.8438188]

It couldn't possibly be simplified to [math] E[Y|X] [/math] because
[math] Y\mapsto c·Y[/math]
gives
[math] E[c·Y|X] = c·E[Y|X] [/math]
and a factor
[math] c^2 [/math]
for your expression.

Besides, for independence of X, isn't this just the variance? Your claim would be the variance equals the expectation.