Relation betweeen expected area of square and rectangle
Clash Royale CLAN TAG#URR8PPP
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Hello I am struggling with the following question, can anybody help please?
Consider a positive real valued random variable $X$
Experiment A: Draw a sample of $X$ and create a square with it as the edge length, and call this square $S$.
Experiment B: Draw two independent samples of $X$ and create a rectangle with these two as sides, and call this rectangle $R$. Let
$$A = E[textArea(S)] (E - textExpectation)$$
and
$$B = E[textArea(R)]$$
What is relation between $A$ and $B$?
Edit: I have no idea how to approach this kind of questions any help is highly appreciated.
probability expected-value
edited Sep 6 at 9:22
Riccardo Ceccon
877320
asked Sep 6 at 7:45
Anurag Shah
32
add a comment |Â
up vote
0
down vote
favorite
Hello I am struggling with the following question, can anybody help please?
Consider a positive real valued random variable $X$
Experiment A: Draw a sample of $X$ and create a square with it as the edge length, and call this square $S$.
Experiment B: Draw two independent samples of $X$ and create a rectangle with these two as sides, and call this rectangle $R$. Let
$$A = E[textArea(S)] (E - textExpectation)$$
and
$$B = E[textArea(R)]$$
What is relation between $A$ and $B$?
Edit: I have no idea how to approach this kind of questions any help is highly appreciated.
probability expected-value
edited Sep 6 at 9:22
Riccardo Ceccon
877320
asked Sep 6 at 7:45
Anurag Shah
32
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Sep 6 at 7:52
1
As mentioned above, at least you should try to express those area in terms of $X, X_1, X_2$ etc.
– BGM
Sep 6 at 8:01
Hi! What do you mean by $E-Expectation?$
– Riccardo Ceccon
Sep 6 at 8:12
Hmm I found this question interesting it seems that the expected area of the square could be way bigger than the expected area of the rectangle if the variance of $X$ is super big...
– HJ_beginner
Sep 6 at 8:26
1
@RiccardoCeccon I just meant that E(x) means Expectation of x
– Anurag Shah
Sep 6 at 8:47
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Hello I am struggling with the following question, can anybody help please?
Consider a positive real valued random variable $X$
Experiment A: Draw a sample of $X$ and create a square with it as the edge length, and call this square $S$.
Experiment B: Draw two independent samples of $X$ and create a rectangle with these two as sides, and call this rectangle $R$. Let
$$A = E[textArea(S)] (E - textExpectation)$$
and
$$B = E[textArea(R)]$$
What is relation between $A$ and $B$?
Edit: I have no idea how to approach this kind of questions any help is highly appreciated.
probability expected-value
edited Sep 6 at 9:22
Riccardo Ceccon
877320
asked Sep 6 at 7:45
Anurag Shah
32
Hello I am struggling with the following question, can anybody help please?
Consider a positive real valued random variable $X$
Experiment A: Draw a sample of $X$ and create a square with it as the edge length, and call this square $S$.
Experiment B: Draw two independent samples of $X$ and create a rectangle with these two as sides, and call this rectangle $R$. Let
$$A = E[textArea(S)] (E - textExpectation)$$
and
$$B = E[textArea(R)]$$
What is relation between $A$ and $B$?
Edit: I have no idea how to approach this kind of questions any help is highly appreciated.
probability expected-value
probability expected-value
edited Sep 6 at 9:22
Riccardo Ceccon
877320
asked Sep 6 at 7:45
Anurag Shah
32
edited Sep 6 at 9:22
Riccardo Ceccon
877320
asked Sep 6 at 7:45
Anurag Shah
32
edited Sep 6 at 9:22
Riccardo Ceccon
877320
edited Sep 6 at 9:22
Riccardo Ceccon
877320
edited Sep 6 at 9:22
Riccardo Ceccon
877320
877320
asked Sep 6 at 7:45
Anurag Shah
32
asked Sep 6 at 7:45
Anurag Shah
32
asked Sep 6 at 7:45
Anurag Shah
32
32
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Sep 6 at 7:52
1
As mentioned above, at least you should try to express those area in terms of $X, X_1, X_2$ etc.
– BGM
Sep 6 at 8:01
Hi! What do you mean by $E-Expectation?$
– Riccardo Ceccon
Sep 6 at 8:12
Hmm I found this question interesting it seems that the expected area of the square could be way bigger than the expected area of the rectangle if the variance of $X$ is super big...
– HJ_beginner
Sep 6 at 8:26
1
@RiccardoCeccon I just meant that E(x) means Expectation of x
– Anurag Shah
Sep 6 at 8:47
add a comment |Â
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Sep 6 at 7:52
1
As mentioned above, at least you should try to express those area in terms of $X, X_1, X_2$ etc.
– BGM
Sep 6 at 8:01
Hi! What do you mean by $E-Expectation?$
– Riccardo Ceccon
Sep 6 at 8:12
Hmm I found this question interesting it seems that the expected area of the square could be way bigger than the expected area of the rectangle if the variance of $X$ is super big...
– HJ_beginner
Sep 6 at 8:26
1
@RiccardoCeccon I just meant that E(x) means Expectation of x
– Anurag Shah
Sep 6 at 8:47
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Sep 6 at 7:52
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Sep 6 at 7:52
1
1
As mentioned above, at least you should try to express those area in terms of $X, X_1, X_2$ etc.
– BGM
Sep 6 at 8:01
As mentioned above, at least you should try to express those area in terms of $X, X_1, X_2$ etc.
– BGM
Sep 6 at 8:01
Hi! What do you mean by $E-Expectation?$
– Riccardo Ceccon
Sep 6 at 8:12
Hi! What do you mean by $E-Expectation?$
– Riccardo Ceccon
Sep 6 at 8:12
Hmm I found this question interesting it seems that the expected area of the square could be way bigger than the expected area of the rectangle if the variance of $X$ is super big...
– HJ_beginner
Sep 6 at 8:26
Hmm I found this question interesting it seems that the expected area of the square could be way bigger than the expected area of the rectangle if the variance of $X$ is super big...
– HJ_beginner
Sep 6 at 8:26
1
1
@RiccardoCeccon I just meant that E(x) means Expectation of x
– Anurag Shah
Sep 6 at 8:47
@RiccardoCeccon I just meant that E(x) means Expectation of x
– Anurag Shah
Sep 6 at 8:47
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Hint: $A=E(X_1^2)$ and $B=E(X_1X_2)=E(X_1)E(X_2)=E^2(X_1)$
answered Sep 6 at 8:30
Yuta
62929
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
1
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Hint: $A=E(X_1^2)$ and $B=E(X_1X_2)=E(X_1)E(X_2)=E^2(X_1)$
answered Sep 6 at 8:30
Yuta
62929
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
1
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
add a comment |Â
up vote
1
down vote
accepted
Hint: $A=E(X_1^2)$ and $B=E(X_1X_2)=E(X_1)E(X_2)=E^2(X_1)$
answered Sep 6 at 8:30
Yuta
62929
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
1
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Hint: $A=E(X_1^2)$ and $B=E(X_1X_2)=E(X_1)E(X_2)=E^2(X_1)$
answered Sep 6 at 8:30
Yuta
62929
Hint: $A=E(X_1^2)$ and $B=E(X_1X_2)=E(X_1)E(X_2)=E^2(X_1)$
answered Sep 6 at 8:30
Yuta
62929
answered Sep 6 at 8:30
Yuta
62929
answered Sep 6 at 8:30
Yuta
62929
answered Sep 6 at 8:30
Yuta
62929
62929
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
1
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
add a comment |Â
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
1
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
Ok so as E(X^2) >= E(X)^2 we can conclude A >= B. Correct me if I'm wrong.
– Anurag Shah
Sep 6 at 8:46
1
1
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
And the difference $A-B$ is actually the variance of $X$. Did you notice?
– Yuta
Sep 6 at 9:25
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
yeah from that observation I remembered this result of inequality!
– Anurag Shah
Sep 6 at 9:33
add a comment |Â
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Sep 6 at 7:52
1
As mentioned above, at least you should try to express those area in terms of $X, X_1, X_2$ etc.
– BGM
Sep 6 at 8:01
Hi! What do you mean by $E-Expectation?$
– Riccardo Ceccon
Sep 6 at 8:12
Hmm I found this question interesting it seems that the expected area of the square could be way bigger than the expected area of the rectangle if the variance of $X$ is super big...
– HJ_beginner
Sep 6 at 8:26
1
@RiccardoCeccon I just meant that E(x) means Expectation of x
– Anurag Shah
Sep 6 at 8:47