Mixing
Are these two probability equal or not? [closed]
Suppose there is a distribution $D$.
$x$ is extracted directly from $D$.
$s = (a_1,a_2,dots,a_n)$ is $n$ samples i.i.d from $D$.
then extract a sample $y$ from $s$.
Can $y$ be interpreted as being extracted directly from $D$?
I mean, $x$ and $y$ have same meaning?
probability probability-distributions
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
asked Nov 20 '18 at 0:17
zhm1995
84
closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Suppose there is a distribution $D$.
$x$ is extracted directly from $D$.
$s = (a_1,a_2,dots,a_n)$ is $n$ samples i.i.d from $D$.
then extract a sample $y$ from $s$.
Can $y$ be interpreted as being extracted directly from $D$?
I mean, $x$ and $y$ have same meaning?
probability probability-distributions
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
asked Nov 20 '18 at 0:17
zhm1995
84
closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
3
It sounds like you are asking something like "Is the probability that you get an ace of spades you select a single card from a standard deck of cards the same as the probability that you get an ace of spades if you select a single card from a hand of several cards which itself was randomly selected from a standard deck of cards." If that is what you are asking, the answer is yes. It is difficult to tell if this is what you are trying to get at due to several grammatical errors and lack of clarity when trying to get concepts across.
– JMoravitz
Nov 20 '18 at 0:23
add a comment |
Suppose there is a distribution $D$.
$x$ is extracted directly from $D$.
$s = (a_1,a_2,dots,a_n)$ is $n$ samples i.i.d from $D$.
then extract a sample $y$ from $s$.
Can $y$ be interpreted as being extracted directly from $D$?
I mean, $x$ and $y$ have same meaning?
probability probability-distributions
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
asked Nov 20 '18 at 0:17
zhm1995
84
Suppose there is a distribution $D$.
$x$ is extracted directly from $D$.
$s = (a_1,a_2,dots,a_n)$ is $n$ samples i.i.d from $D$.
then extract a sample $y$ from $s$.
Can $y$ be interpreted as being extracted directly from $D$?
I mean, $x$ and $y$ have same meaning?
probability probability-distributions
probability probability-distributions
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
asked Nov 20 '18 at 0:17
zhm1995
84
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
asked Nov 20 '18 at 0:17
zhm1995
84
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
edited Nov 20 '18 at 1:01
Tianlalu
3,09621038
3,09621038
asked Nov 20 '18 at 0:17
zhm1995
84
asked Nov 20 '18 at 0:17
zhm1995
84
asked Nov 20 '18 at 0:17
zhm1995
84
84
closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 '18 at 8:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
3
It sounds like you are asking something like "Is the probability that you get an ace of spades you select a single card from a standard deck of cards the same as the probability that you get an ace of spades if you select a single card from a hand of several cards which itself was randomly selected from a standard deck of cards." If that is what you are asking, the answer is yes. It is difficult to tell if this is what you are trying to get at due to several grammatical errors and lack of clarity when trying to get concepts across.
– JMoravitz
Nov 20 '18 at 0:23
add a comment |
3
It sounds like you are asking something like "Is the probability that you get an ace of spades you select a single card from a standard deck of cards the same as the probability that you get an ace of spades if you select a single card from a hand of several cards which itself was randomly selected from a standard deck of cards." If that is what you are asking, the answer is yes. It is difficult to tell if this is what you are trying to get at due to several grammatical errors and lack of clarity when trying to get concepts across.
– JMoravitz
Nov 20 '18 at 0:23
3
3
It sounds like you are asking something like "Is the probability that you get an ace of spades you select a single card from a standard deck of cards the same as the probability that you get an ace of spades if you select a single card from a hand of several cards which itself was randomly selected from a standard deck of cards." If that is what you are asking, the answer is yes. It is difficult to tell if this is what you are trying to get at due to several grammatical errors and lack of clarity when trying to get concepts across.
– JMoravitz
Nov 20 '18 at 0:23
It sounds like you are asking something like "Is the probability that you get an ace of spades you select a single card from a standard deck of cards the same as the probability that you get an ace of spades if you select a single card from a hand of several cards which itself was randomly selected from a standard deck of cards." If that is what you are asking, the answer is yes. It is difficult to tell if this is what you are trying to get at due to several grammatical errors and lack of clarity when trying to get concepts across.
– JMoravitz
Nov 20 '18 at 0:23
add a comment |
1 Answer
1
active
oldest
votes
Yes. It matters not how many sample you generate.
Since each set of samples in $(a_k)_{1leq kleq n}$ is selected independently and identically from $D$ (ie with replacement after each sampling), therefore it does not matter which sample you select $y$ from, it has the same probability of having a particular identity as if you had selected it dirrectly from from $D$.
Take a standard deck of 52 cards. Draw a hand of five cards, record it as $a_1$, replace it, shuffle and draw another, recording it as $a_2$, and so forth. Among $n$ such drawings you pick an index from 1 to $n$ without bias, then select one of the cards in that indexed hand. The probability that that card is the ace of clubs is: $1/52$, exactly as if you had drawn a single card straight from the deck.
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Yes. It matters not how many sample you generate.
Since each set of samples in $(a_k)_{1leq kleq n}$ is selected independently and identically from $D$ (ie with replacement after each sampling), therefore it does not matter which sample you select $y$ from, it has the same probability of having a particular identity as if you had selected it dirrectly from from $D$.
Take a standard deck of 52 cards. Draw a hand of five cards, record it as $a_1$, replace it, shuffle and draw another, recording it as $a_2$, and so forth. Among $n$ such drawings you pick an index from 1 to $n$ without bias, then select one of the cards in that indexed hand. The probability that that card is the ace of clubs is: $1/52$, exactly as if you had drawn a single card straight from the deck.
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
add a comment |
Yes. It matters not how many sample you generate.
Since each set of samples in $(a_k)_{1leq kleq n}$ is selected independently and identically from $D$ (ie with replacement after each sampling), therefore it does not matter which sample you select $y$ from, it has the same probability of having a particular identity as if you had selected it dirrectly from from $D$.
Take a standard deck of 52 cards. Draw a hand of five cards, record it as $a_1$, replace it, shuffle and draw another, recording it as $a_2$, and so forth. Among $n$ such drawings you pick an index from 1 to $n$ without bias, then select one of the cards in that indexed hand. The probability that that card is the ace of clubs is: $1/52$, exactly as if you had drawn a single card straight from the deck.
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
add a comment |
Yes. It matters not how many sample you generate.
Since each set of samples in $(a_k)_{1leq kleq n}$ is selected independently and identically from $D$ (ie with replacement after each sampling), therefore it does not matter which sample you select $y$ from, it has the same probability of having a particular identity as if you had selected it dirrectly from from $D$.
Take a standard deck of 52 cards. Draw a hand of five cards, record it as $a_1$, replace it, shuffle and draw another, recording it as $a_2$, and so forth. Among $n$ such drawings you pick an index from 1 to $n$ without bias, then select one of the cards in that indexed hand. The probability that that card is the ace of clubs is: $1/52$, exactly as if you had drawn a single card straight from the deck.
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
Yes. It matters not how many sample you generate.
Since each set of samples in $(a_k)_{1leq kleq n}$ is selected independently and identically from $D$ (ie with replacement after each sampling), therefore it does not matter which sample you select $y$ from, it has the same probability of having a particular identity as if you had selected it dirrectly from from $D$.
Take a standard deck of 52 cards. Draw a hand of five cards, record it as $a_1$, replace it, shuffle and draw another, recording it as $a_2$, and so forth. Among $n$ such drawings you pick an index from 1 to $n$ without bias, then select one of the cards in that indexed hand. The probability that that card is the ace of clubs is: $1/52$, exactly as if you had drawn a single card straight from the deck.
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
answered Nov 20 '18 at 0:52
Graham Kemp
84.7k43378
84.7k43378
add a comment |
add a comment |
3
It sounds like you are asking something like "Is the probability that you get an ace of spades you select a single card from a standard deck of cards the same as the probability that you get an ace of spades if you select a single card from a hand of several cards which itself was randomly selected from a standard deck of cards." If that is what you are asking, the answer is yes. It is difficult to tell if this is what you are trying to get at due to several grammatical errors and lack of clarity when trying to get concepts across.
– JMoravitz
Nov 20 '18 at 0:23