Mixing
Interpretation of a sample space problem
$A, B$ and $C$ take turns in flipping a coin. The first one to get a head wins. The sample space of this experiment is as given:
$S = {1, 01, 001, 0001, dots ,\0000}$
Then how can I interpret the sample space? I cannot understand that $0000$ case in the sample space. Does it mean that none wins? If it means that, then should not it be excluded from $S$ and included in $S^c$?
Please help me by explaining this topic. Thanks in advance.
probability
asked Nov 21 '18 at 5:21
user587389
327
add a comment |
$A, B$ and $C$ take turns in flipping a coin. The first one to get a head wins. The sample space of this experiment is as given:
$S = {1, 01, 001, 0001, dots ,\0000}$
Then how can I interpret the sample space? I cannot understand that $0000$ case in the sample space. Does it mean that none wins? If it means that, then should not it be excluded from $S$ and included in $S^c$?
Please help me by explaining this topic. Thanks in advance.
probability
asked Nov 21 '18 at 5:21
user587389
327
The last one doesn't make sense as written: four tails and then stop. Surely they are supposed to keep going. Was it actually supposed to be "$0000ldots$", that is, an infinite sequence of all tails?
– David K
Nov 21 '18 at 6:19
yes, it means an infinite sequence of all tails. But why is it included in S? I can't get it.
– user587389
Nov 21 '18 at 9:20
If this case weren't included, someone else might complain that the author had not considered what happens if the players only get tails. Answer: they just keep flipping the coin forever. But since we assign zero probability to that event, it has no impact on the calculations.
– David K
Nov 21 '18 at 12:41
Oh, Thanks Sir. Now I get it.
– user587389
Nov 21 '18 at 13:18
add a comment |
$A, B$ and $C$ take turns in flipping a coin. The first one to get a head wins. The sample space of this experiment is as given:
$S = {1, 01, 001, 0001, dots ,\0000}$
Then how can I interpret the sample space? I cannot understand that $0000$ case in the sample space. Does it mean that none wins? If it means that, then should not it be excluded from $S$ and included in $S^c$?
Please help me by explaining this topic. Thanks in advance.
probability
asked Nov 21 '18 at 5:21
user587389
327
$A, B$ and $C$ take turns in flipping a coin. The first one to get a head wins. The sample space of this experiment is as given:
$S = {1, 01, 001, 0001, dots ,\0000}$
Then how can I interpret the sample space? I cannot understand that $0000$ case in the sample space. Does it mean that none wins? If it means that, then should not it be excluded from $S$ and included in $S^c$?
Please help me by explaining this topic. Thanks in advance.
probability
probability
asked Nov 21 '18 at 5:21
user587389
327
asked Nov 21 '18 at 5:21
user587389
327
asked Nov 21 '18 at 5:21
user587389
327
asked Nov 21 '18 at 5:21
user587389
327
asked Nov 21 '18 at 5:21
user587389
327
327
The last one doesn't make sense as written: four tails and then stop. Surely they are supposed to keep going. Was it actually supposed to be "$0000ldots$", that is, an infinite sequence of all tails?
– David K
Nov 21 '18 at 6:19
yes, it means an infinite sequence of all tails. But why is it included in S? I can't get it.
– user587389
Nov 21 '18 at 9:20
If this case weren't included, someone else might complain that the author had not considered what happens if the players only get tails. Answer: they just keep flipping the coin forever. But since we assign zero probability to that event, it has no impact on the calculations.
– David K
Nov 21 '18 at 12:41
Oh, Thanks Sir. Now I get it.
– user587389
Nov 21 '18 at 13:18
add a comment |
The last one doesn't make sense as written: four tails and then stop. Surely they are supposed to keep going. Was it actually supposed to be "$0000ldots$", that is, an infinite sequence of all tails?
– David K
Nov 21 '18 at 6:19
yes, it means an infinite sequence of all tails. But why is it included in S? I can't get it.
– user587389
Nov 21 '18 at 9:20
If this case weren't included, someone else might complain that the author had not considered what happens if the players only get tails. Answer: they just keep flipping the coin forever. But since we assign zero probability to that event, it has no impact on the calculations.
– David K
Nov 21 '18 at 12:41
Oh, Thanks Sir. Now I get it.
– user587389
Nov 21 '18 at 13:18
The last one doesn't make sense as written: four tails and then stop. Surely they are supposed to keep going. Was it actually supposed to be "$0000ldots$", that is, an infinite sequence of all tails?
– David K
Nov 21 '18 at 6:19
The last one doesn't make sense as written: four tails and then stop. Surely they are supposed to keep going. Was it actually supposed to be "$0000ldots$", that is, an infinite sequence of all tails?
– David K
Nov 21 '18 at 6:19
yes, it means an infinite sequence of all tails. But why is it included in S? I can't get it.
– user587389
Nov 21 '18 at 9:20
yes, it means an infinite sequence of all tails. But why is it included in S? I can't get it.
– user587389
Nov 21 '18 at 9:20
If this case weren't included, someone else might complain that the author had not considered what happens if the players only get tails. Answer: they just keep flipping the coin forever. But since we assign zero probability to that event, it has no impact on the calculations.
– David K
Nov 21 '18 at 12:41
If this case weren't included, someone else might complain that the author had not considered what happens if the players only get tails. Answer: they just keep flipping the coin forever. But since we assign zero probability to that event, it has no impact on the calculations.
– David K
Nov 21 '18 at 12:41
Oh, Thanks Sir. Now I get it.
– user587389
Nov 21 '18 at 13:18
Oh, Thanks Sir. Now I get it.
– user587389
Nov 21 '18 at 13:18
add a comment |
1 Answer
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The sample space is indeed given by
$$S=bigl{0^k 1bigm| kin{mathbb N}_{geq0}bigr} cup{000ldots} .$$
Fate selects a point $omegain S$. The points $omega=0^k1$ have a probability $p_k>0$, whereas the special point $omega=000ldots$ has probability $p_infty=0$.
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
add a comment |
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1 Answer
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1 Answer
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active
oldest
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oldest
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active
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The sample space is indeed given by
$$S=bigl{0^k 1bigm| kin{mathbb N}_{geq0}bigr} cup{000ldots} .$$
Fate selects a point $omegain S$. The points $omega=0^k1$ have a probability $p_k>0$, whereas the special point $omega=000ldots$ has probability $p_infty=0$.
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
add a comment |
The sample space is indeed given by
$$S=bigl{0^k 1bigm| kin{mathbb N}_{geq0}bigr} cup{000ldots} .$$
Fate selects a point $omegain S$. The points $omega=0^k1$ have a probability $p_k>0$, whereas the special point $omega=000ldots$ has probability $p_infty=0$.
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
add a comment |
The sample space is indeed given by
$$S=bigl{0^k 1bigm| kin{mathbb N}_{geq0}bigr} cup{000ldots} .$$
Fate selects a point $omegain S$. The points $omega=0^k1$ have a probability $p_k>0$, whereas the special point $omega=000ldots$ has probability $p_infty=0$.
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
The sample space is indeed given by
$$S=bigl{0^k 1bigm| kin{mathbb N}_{geq0}bigr} cup{000ldots} .$$
Fate selects a point $omegain S$. The points $omega=0^k1$ have a probability $p_k>0$, whereas the special point $omega=000ldots$ has probability $p_infty=0$.
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
answered Nov 21 '18 at 12:06
Christian Blatter
172k7112326
172k7112326
add a comment |
add a comment |
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The last one doesn't make sense as written: four tails and then stop. Surely they are supposed to keep going. Was it actually supposed to be "$0000ldots$", that is, an infinite sequence of all tails?
– David K
Nov 21 '18 at 6:19
yes, it means an infinite sequence of all tails. But why is it included in S? I can't get it.
– user587389
Nov 21 '18 at 9:20
If this case weren't included, someone else might complain that the author had not considered what happens if the players only get tails. Answer: they just keep flipping the coin forever. But since we assign zero probability to that event, it has no impact on the calculations.
– David K
Nov 21 '18 at 12:41
Oh, Thanks Sir. Now I get it.
– user587389
Nov 21 '18 at 13:18