Calculating a conditional expectation (probability theory)
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Let $X$ and $Y$ be two random variables with the joint probability density function $f_{xy}(x,y)=(15/4) x y^2$ for $0 < 2 y leq x leq 2$ and $0$ otherwise.
Calculate ${cal E}[X^2+Y^2 leq 1 | X geq 0.5]$
probability conditional-expectation
edited Nov 19 at 19:30
David G. Stork
9,30721232
asked Nov 19 at 19:16
amirkard
12
add a comment |
up vote
0
down vote
favorite
Let $X$ and $Y$ be two random variables with the joint probability density function $f_{xy}(x,y)=(15/4) x y^2$ for $0 < 2 y leq x leq 2$ and $0$ otherwise.
Calculate ${cal E}[X^2+Y^2 leq 1 | X geq 0.5]$
probability conditional-expectation
edited Nov 19 at 19:30
David G. Stork
9,30721232
asked Nov 19 at 19:16
amirkard
12
1
But you must have tried something. Could you show your work first?
– StubbornAtom
Nov 19 at 19:20
1
I am a beginner... but are you supposed to calculate $E[X^2+Y^2 le 1 | X geq 0.5]$ or $P[X^2+Y^2 le 1 | X ge 0.5]$ I've seen questions that ask to calculate $E[g(X,Y) mid A]$ but not when $g(X,Y)$ is a statement like that. Again I'm a noob
– HJ_beginner
Nov 19 at 19:35
Hi,thanks for your answer.Iam supposed to calculate expectation not probability and what you mentioned is exactly where i don't understand. I mean expectation of an event conditioned on another event that's the reason i cannot solve this
– amirkard
Nov 19 at 20:26
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $X$ and $Y$ be two random variables with the joint probability density function $f_{xy}(x,y)=(15/4) x y^2$ for $0 < 2 y leq x leq 2$ and $0$ otherwise.
Calculate ${cal E}[X^2+Y^2 leq 1 | X geq 0.5]$
probability conditional-expectation
edited Nov 19 at 19:30
David G. Stork
9,30721232
asked Nov 19 at 19:16
amirkard
12
Let $X$ and $Y$ be two random variables with the joint probability density function $f_{xy}(x,y)=(15/4) x y^2$ for $0 < 2 y leq x leq 2$ and $0$ otherwise.
Calculate ${cal E}[X^2+Y^2 leq 1 | X geq 0.5]$
probability conditional-expectation
probability conditional-expectation
edited Nov 19 at 19:30
David G. Stork
9,30721232
asked Nov 19 at 19:16
amirkard
12
edited Nov 19 at 19:30
David G. Stork
9,30721232
asked Nov 19 at 19:16
amirkard
12
edited Nov 19 at 19:30
David G. Stork
9,30721232
edited Nov 19 at 19:30
David G. Stork
9,30721232
edited Nov 19 at 19:30
David G. Stork
9,30721232
9,30721232
asked Nov 19 at 19:16
amirkard
12
asked Nov 19 at 19:16
amirkard
12
asked Nov 19 at 19:16
amirkard
12
12
1
But you must have tried something. Could you show your work first?
– StubbornAtom
Nov 19 at 19:20
1
I am a beginner... but are you supposed to calculate $E[X^2+Y^2 le 1 | X geq 0.5]$ or $P[X^2+Y^2 le 1 | X ge 0.5]$ I've seen questions that ask to calculate $E[g(X,Y) mid A]$ but not when $g(X,Y)$ is a statement like that. Again I'm a noob
– HJ_beginner
Nov 19 at 19:35
Hi,thanks for your answer.Iam supposed to calculate expectation not probability and what you mentioned is exactly where i don't understand. I mean expectation of an event conditioned on another event that's the reason i cannot solve this
– amirkard
Nov 19 at 20:26
add a comment |
1
But you must have tried something. Could you show your work first?
– StubbornAtom
Nov 19 at 19:20
1
I am a beginner... but are you supposed to calculate $E[X^2+Y^2 le 1 | X geq 0.5]$ or $P[X^2+Y^2 le 1 | X ge 0.5]$ I've seen questions that ask to calculate $E[g(X,Y) mid A]$ but not when $g(X,Y)$ is a statement like that. Again I'm a noob
– HJ_beginner
Nov 19 at 19:35
Hi,thanks for your answer.Iam supposed to calculate expectation not probability and what you mentioned is exactly where i don't understand. I mean expectation of an event conditioned on another event that's the reason i cannot solve this
– amirkard
Nov 19 at 20:26
1
1
But you must have tried something. Could you show your work first?
– StubbornAtom
Nov 19 at 19:20
But you must have tried something. Could you show your work first?
– StubbornAtom
Nov 19 at 19:20
1
1
I am a beginner... but are you supposed to calculate $E[X^2+Y^2 le 1 | X geq 0.5]$ or $P[X^2+Y^2 le 1 | X ge 0.5]$ I've seen questions that ask to calculate $E[g(X,Y) mid A]$ but not when $g(X,Y)$ is a statement like that. Again I'm a noob
– HJ_beginner
Nov 19 at 19:35
I am a beginner... but are you supposed to calculate $E[X^2+Y^2 le 1 | X geq 0.5]$ or $P[X^2+Y^2 le 1 | X ge 0.5]$ I've seen questions that ask to calculate $E[g(X,Y) mid A]$ but not when $g(X,Y)$ is a statement like that. Again I'm a noob
– HJ_beginner
Nov 19 at 19:35
Hi,thanks for your answer.Iam supposed to calculate expectation not probability and what you mentioned is exactly where i don't understand. I mean expectation of an event conditioned on another event that's the reason i cannot solve this
– amirkard
Nov 19 at 20:26
Hi,thanks for your answer.Iam supposed to calculate expectation not probability and what you mentioned is exactly where i don't understand. I mean expectation of an event conditioned on another event that's the reason i cannot solve this
– amirkard
Nov 19 at 20:26
add a comment |
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1
But you must have tried something. Could you show your work first?
– StubbornAtom
Nov 19 at 19:20
1
I am a beginner... but are you supposed to calculate $E[X^2+Y^2 le 1 | X geq 0.5]$ or $P[X^2+Y^2 le 1 | X ge 0.5]$ I've seen questions that ask to calculate $E[g(X,Y) mid A]$ but not when $g(X,Y)$ is a statement like that. Again I'm a noob
– HJ_beginner
Nov 19 at 19:35
Hi,thanks for your answer.Iam supposed to calculate expectation not probability and what you mentioned is exactly where i don't understand. I mean expectation of an event conditioned on another event that's the reason i cannot solve this
– amirkard
Nov 19 at 20:26