Working out expectation of a random sample.
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I have the problem:
Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has
mean $μ$ and variance $σ^2$.
Find $mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T
= k[(X_1-X_2)^2 + (X_3-X_4)^2]$ is an unbiased estimator of $σ^2$.
How would I go about this? I have no clue
statistics random sampling
edited Nov 16 at 13:17
callculus
17.6k31427
asked Nov 16 at 12:47
OrangeSegments
384
add a comment |
up vote
0
down vote
favorite
I have the problem:
Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has
mean $μ$ and variance $σ^2$.
Find $mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T
= k[(X_1-X_2)^2 + (X_3-X_4)^2]$ is an unbiased estimator of $σ^2$.
How would I go about this? I have no clue
statistics random sampling
edited Nov 16 at 13:17
callculus
17.6k31427
asked Nov 16 at 12:47
OrangeSegments
384
Are the random variables dependent or independent?
– callculus
Nov 16 at 13:03
@callculus It doesn't specify whether they're dependent or independent but I would assume the latter.
– OrangeSegments
Nov 16 at 13:46
Random sample implies independence in general. Do you know what do you have to do? Where are you stuck?
– StubbornAtom
Nov 16 at 14:36
@stubbornatom I honestly have no clue where to even start. I know E(X1)=E(X2) = μ but that’s the furthest I’ve been able to do
– OrangeSegments
Nov 17 at 3:58
What is the definition of unbiased estimator?
– StubbornAtom
Nov 17 at 7:14
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have the problem:
Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has
mean $μ$ and variance $σ^2$.
Find $mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T
= k[(X_1-X_2)^2 + (X_3-X_4)^2]$ is an unbiased estimator of $σ^2$.
How would I go about this? I have no clue
statistics random sampling
edited Nov 16 at 13:17
callculus
17.6k31427
asked Nov 16 at 12:47
OrangeSegments
384
I have the problem:
Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has
mean $μ$ and variance $σ^2$.
Find $mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T
= k[(X_1-X_2)^2 + (X_3-X_4)^2]$ is an unbiased estimator of $σ^2$.
How would I go about this? I have no clue
statistics random sampling
statistics random sampling
edited Nov 16 at 13:17
callculus
17.6k31427
asked Nov 16 at 12:47
OrangeSegments
384
edited Nov 16 at 13:17
callculus
17.6k31427
asked Nov 16 at 12:47
OrangeSegments
384
edited Nov 16 at 13:17
callculus
17.6k31427
edited Nov 16 at 13:17
callculus
17.6k31427
edited Nov 16 at 13:17
callculus
17.6k31427
17.6k31427
asked Nov 16 at 12:47
OrangeSegments
384
asked Nov 16 at 12:47
OrangeSegments
384
asked Nov 16 at 12:47
OrangeSegments
384
384
Are the random variables dependent or independent?
– callculus
Nov 16 at 13:03
@callculus It doesn't specify whether they're dependent or independent but I would assume the latter.
– OrangeSegments
Nov 16 at 13:46
Random sample implies independence in general. Do you know what do you have to do? Where are you stuck?
– StubbornAtom
Nov 16 at 14:36
@stubbornatom I honestly have no clue where to even start. I know E(X1)=E(X2) = μ but that’s the furthest I’ve been able to do
– OrangeSegments
Nov 17 at 3:58
What is the definition of unbiased estimator?
– StubbornAtom
Nov 17 at 7:14
add a comment |
Are the random variables dependent or independent?
– callculus
Nov 16 at 13:03
@callculus It doesn't specify whether they're dependent or independent but I would assume the latter.
– OrangeSegments
Nov 16 at 13:46
Random sample implies independence in general. Do you know what do you have to do? Where are you stuck?
– StubbornAtom
Nov 16 at 14:36
@stubbornatom I honestly have no clue where to even start. I know E(X1)=E(X2) = μ but that’s the furthest I’ve been able to do
– OrangeSegments
Nov 17 at 3:58
What is the definition of unbiased estimator?
– StubbornAtom
Nov 17 at 7:14
Are the random variables dependent or independent?
– callculus
Nov 16 at 13:03
Are the random variables dependent or independent?
– callculus
Nov 16 at 13:03
@callculus It doesn't specify whether they're dependent or independent but I would assume the latter.
– OrangeSegments
Nov 16 at 13:46
@callculus It doesn't specify whether they're dependent or independent but I would assume the latter.
– OrangeSegments
Nov 16 at 13:46
Random sample implies independence in general. Do you know what do you have to do? Where are you stuck?
– StubbornAtom
Nov 16 at 14:36
Random sample implies independence in general. Do you know what do you have to do? Where are you stuck?
– StubbornAtom
Nov 16 at 14:36
@stubbornatom I honestly have no clue where to even start. I know E(X1)=E(X2) = μ but that’s the furthest I’ve been able to do
– OrangeSegments
Nov 17 at 3:58
@stubbornatom I honestly have no clue where to even start. I know E(X1)=E(X2) = μ but that’s the furthest I’ve been able to do
– OrangeSegments
Nov 17 at 3:58
What is the definition of unbiased estimator?
– StubbornAtom
Nov 17 at 7:14
What is the definition of unbiased estimator?
– StubbornAtom
Nov 17 at 7:14
add a comment |
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Are the random variables dependent or independent?
– callculus
Nov 16 at 13:03
@callculus It doesn't specify whether they're dependent or independent but I would assume the latter.
– OrangeSegments
Nov 16 at 13:46
Random sample implies independence in general. Do you know what do you have to do? Where are you stuck?
– StubbornAtom
Nov 16 at 14:36
@stubbornatom I honestly have no clue where to even start. I know E(X1)=E(X2) = μ but that’s the furthest I’ve been able to do
– OrangeSegments
Nov 17 at 3:58
What is the definition of unbiased estimator?
– StubbornAtom
Nov 17 at 7:14