Are these two probability equal or not? [closed]











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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?










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closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 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 at 0:23















up vote
-1
down vote

favorite












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?










share|cite|improve this question















closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 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 at 0:23













up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











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?










share|cite|improve this question















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






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edited Nov 20 at 1:01









Tianlalu

3,0001937




3,0001937










asked Nov 20 at 0:17









zhm1995

84




84




closed as unclear what you're asking by JMoravitz, Leucippus, max_zorn, KReiser, mau Nov 20 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 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 at 0:23














  • 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 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 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 at 0:23










1 Answer
1






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0
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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.






share|cite|improve this answer




























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    down vote



    accepted










    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.






    share|cite|improve this answer

























      up vote
      0
      down vote



      accepted










      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.






      share|cite|improve this answer























        up vote
        0
        down vote



        accepted







        up vote
        0
        down vote



        accepted






        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.






        share|cite|improve this answer












        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 20 at 0:52









        Graham Kemp

        84.6k43378




        84.6k43378















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