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Question regarding the mean of independently (not identically ) distributed random variables?
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Hi i have the following question which may be a simple question for majority of the people. But i need to know the difference clearly ..
Let $X_1 ,...X_n$ be independently distributed (not identically) random variables with distribution of $ ~ uniform [0,n]$ .
I need to find the expectation of $ sum_k=1^n X_k$
Since the distribution is $uniform$ , $E(X_k)= n/2$ . So $E(sum_k=1^n X_k) = sum_k=1^n E(X_k) $ = $sum_k=1^n n/2$ .
Since the variables are only independently distributed, can i further simplify to $(n* n/2 )$ or do i need to stop from $sum_k=1^n n/2$.
Also if the variables are $IID$ , then is $E(sum_k=1^n X_k) = n* n/2 = n^2/2 $ ?
Thank you
summation random-variables expectation
asked Jul 15 at 20:22
Stat lover
4411
add a comment |Â
up vote
0
down vote
favorite
Hi i have the following question which may be a simple question for majority of the people. But i need to know the difference clearly ..
Let $X_1 ,...X_n$ be independently distributed (not identically) random variables with distribution of $ ~ uniform [0,n]$ .
I need to find the expectation of $ sum_k=1^n X_k$
Since the distribution is $uniform$ , $E(X_k)= n/2$ . So $E(sum_k=1^n X_k) = sum_k=1^n E(X_k) $ = $sum_k=1^n n/2$ .
Since the variables are only independently distributed, can i further simplify to $(n* n/2 )$ or do i need to stop from $sum_k=1^n n/2$.
Also if the variables are $IID$ , then is $E(sum_k=1^n X_k) = n* n/2 = n^2/2 $ ?
Thank you
summation random-variables expectation
asked Jul 15 at 20:22
Stat lover
4411
2
Why do you say they are not identically distributed, then that the distribution is $uniform[0,n]$? That is identically distributed.
– Robert Israel
Jul 15 at 20:32
@RobertIsrael the question says nothing about identical distributed. It says only independently distributed
– Stat lover
Jul 15 at 20:38
2
You are over thinking!! $sum_k=1^nc=nc$ when $c$ is constant.
– herb steinberg
Jul 15 at 20:42
1
@Statlover : Related to Robert's comment: Can you give an example of two random variables $A, B$ that are both uniformly distributed over $[0,2]$ but that are not identically distributed? (This is similar to finding an example of two distinct colors that are both green).
– Michael
Jul 16 at 0:31
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Hi i have the following question which may be a simple question for majority of the people. But i need to know the difference clearly ..
Let $X_1 ,...X_n$ be independently distributed (not identically) random variables with distribution of $ ~ uniform [0,n]$ .
I need to find the expectation of $ sum_k=1^n X_k$
Since the distribution is $uniform$ , $E(X_k)= n/2$ . So $E(sum_k=1^n X_k) = sum_k=1^n E(X_k) $ = $sum_k=1^n n/2$ .
Since the variables are only independently distributed, can i further simplify to $(n* n/2 )$ or do i need to stop from $sum_k=1^n n/2$.
Also if the variables are $IID$ , then is $E(sum_k=1^n X_k) = n* n/2 = n^2/2 $ ?
Thank you
summation random-variables expectation
asked Jul 15 at 20:22
Stat lover
4411
Hi i have the following question which may be a simple question for majority of the people. But i need to know the difference clearly ..
Let $X_1 ,...X_n$ be independently distributed (not identically) random variables with distribution of $ ~ uniform [0,n]$ .
I need to find the expectation of $ sum_k=1^n X_k$
Since the distribution is $uniform$ , $E(X_k)= n/2$ . So $E(sum_k=1^n X_k) = sum_k=1^n E(X_k) $ = $sum_k=1^n n/2$ .
Since the variables are only independently distributed, can i further simplify to $(n* n/2 )$ or do i need to stop from $sum_k=1^n n/2$.
Also if the variables are $IID$ , then is $E(sum_k=1^n X_k) = n* n/2 = n^2/2 $ ?
Thank you
summation random-variables expectation
asked Jul 15 at 20:22
Stat lover
4411
asked Jul 15 at 20:22
Stat lover
4411
asked Jul 15 at 20:22
Stat lover
4411
asked Jul 15 at 20:22
Stat lover
4411
4411
2
Why do you say they are not identically distributed, then that the distribution is $uniform[0,n]$? That is identically distributed.
– Robert Israel
Jul 15 at 20:32
@RobertIsrael the question says nothing about identical distributed. It says only independently distributed
– Stat lover
Jul 15 at 20:38
2
You are over thinking!! $sum_k=1^nc=nc$ when $c$ is constant.
– herb steinberg
Jul 15 at 20:42
1
@Statlover : Related to Robert's comment: Can you give an example of two random variables $A, B$ that are both uniformly distributed over $[0,2]$ but that are not identically distributed? (This is similar to finding an example of two distinct colors that are both green).
– Michael
Jul 16 at 0:31
add a comment |Â
2
Why do you say they are not identically distributed, then that the distribution is $uniform[0,n]$? That is identically distributed.
– Robert Israel
Jul 15 at 20:32
@RobertIsrael the question says nothing about identical distributed. It says only independently distributed
– Stat lover
Jul 15 at 20:38
2
You are over thinking!! $sum_k=1^nc=nc$ when $c$ is constant.
– herb steinberg
Jul 15 at 20:42
1
@Statlover : Related to Robert's comment: Can you give an example of two random variables $A, B$ that are both uniformly distributed over $[0,2]$ but that are not identically distributed? (This is similar to finding an example of two distinct colors that are both green).
– Michael
Jul 16 at 0:31
2
2
Why do you say they are not identically distributed, then that the distribution is $uniform[0,n]$? That is identically distributed.
– Robert Israel
Jul 15 at 20:32
Why do you say they are not identically distributed, then that the distribution is $uniform[0,n]$? That is identically distributed.
– Robert Israel
Jul 15 at 20:32
@RobertIsrael the question says nothing about identical distributed. It says only independently distributed
– Stat lover
Jul 15 at 20:38
@RobertIsrael the question says nothing about identical distributed. It says only independently distributed
– Stat lover
Jul 15 at 20:38
2
2
You are over thinking!! $sum_k=1^nc=nc$ when $c$ is constant.
– herb steinberg
Jul 15 at 20:42
You are over thinking!! $sum_k=1^nc=nc$ when $c$ is constant.
– herb steinberg
Jul 15 at 20:42
1
1
@Statlover : Related to Robert's comment: Can you give an example of two random variables $A, B$ that are both uniformly distributed over $[0,2]$ but that are not identically distributed? (This is similar to finding an example of two distinct colors that are both green).
– Michael
Jul 16 at 0:31
@Statlover : Related to Robert's comment: Can you give an example of two random variables $A, B$ that are both uniformly distributed over $[0,2]$ but that are not identically distributed? (This is similar to finding an example of two distinct colors that are both green).
– Michael
Jul 16 at 0:31
add a comment |Â
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2
Why do you say they are not identically distributed, then that the distribution is $uniform[0,n]$? That is identically distributed.
– Robert Israel
Jul 15 at 20:32
@RobertIsrael the question says nothing about identical distributed. It says only independently distributed
– Stat lover
Jul 15 at 20:38
2
You are over thinking!! $sum_k=1^nc=nc$ when $c$ is constant.
– herb steinberg
Jul 15 at 20:42
1
@Statlover : Related to Robert's comment: Can you give an example of two random variables $A, B$ that are both uniformly distributed over $[0,2]$ but that are not identically distributed? (This is similar to finding an example of two distinct colors that are both green).
– Michael
Jul 16 at 0:31