Two aspects of randomness
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Consider a random sequence of integers
1, 4, 3, 8, 2, 5, 3, 8 ...
The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next must be equal to $frac{1}{10}$.
Now consider that we are getting only numbers less than 5 in the sequence, it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more, this does not follow the randomness criteria as numbers are now in some form more predictable.
Do the two aspects of randomness contradict with each other?
Or am I wrong somewhere in this deductive thinking?
probability sequences-and-series statistical-inference random natural-deduction
asked 5 hours ago
mathaholic
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Consider a random sequence of integers
1, 4, 3, 8, 2, 5, 3, 8 ...
The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next must be equal to $frac{1}{10}$.
Now consider that we are getting only numbers less than 5 in the sequence, it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more, this does not follow the randomness criteria as numbers are now in some form more predictable.
Do the two aspects of randomness contradict with each other?
Or am I wrong somewhere in this deductive thinking?
probability sequences-and-series statistical-inference random natural-deduction
asked 5 hours ago
mathaholic
1
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
So, when you write, "integer", what you actually mean is "digit"?
– Gerry Myerson
5 hours ago
add a comment |
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0
down vote
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up vote
0
down vote
favorite
Consider a random sequence of integers
1, 4, 3, 8, 2, 5, 3, 8 ...
The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next must be equal to $frac{1}{10}$.
Now consider that we are getting only numbers less than 5 in the sequence, it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more, this does not follow the randomness criteria as numbers are now in some form more predictable.
Do the two aspects of randomness contradict with each other?
Or am I wrong somewhere in this deductive thinking?
probability sequences-and-series statistical-inference random natural-deduction
asked 5 hours ago
mathaholic
1
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Consider a random sequence of integers
1, 4, 3, 8, 2, 5, 3, 8 ...
The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next must be equal to $frac{1}{10}$.
Now consider that we are getting only numbers less than 5 in the sequence, it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more, this does not follow the randomness criteria as numbers are now in some form more predictable.
Do the two aspects of randomness contradict with each other?
Or am I wrong somewhere in this deductive thinking?
probability sequences-and-series statistical-inference random natural-deduction
probability sequences-and-series statistical-inference random natural-deduction
asked 5 hours ago
mathaholic
1
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
mathaholic
1
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
mathaholic
1
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
mathaholic
1
asked 5 hours ago
mathaholic
1
1
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
mathaholic is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
So, when you write, "integer", what you actually mean is "digit"?
– Gerry Myerson
5 hours ago
add a comment |
2
So, when you write, "integer", what you actually mean is "digit"?
– Gerry Myerson
5 hours ago
2
2
So, when you write, "integer", what you actually mean is "digit"?
– Gerry Myerson
5 hours ago
So, when you write, "integer", what you actually mean is "digit"?
– Gerry Myerson
5 hours ago
add a comment |
1 Answer
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1
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Welcome to MSE,
it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more.
This is not true. If every choice of digits is independent, there is no change in the probabilities for the next digit of the sequence.
You can take a look at this question, which is somehow close to yours.
Does the probability change if you know previous results?
If that's not what you are asking please provide us with more details.
answered 5 hours ago
Gâteau-Gallois
31319
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Welcome to MSE,
it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more.
This is not true. If every choice of digits is independent, there is no change in the probabilities for the next digit of the sequence.
You can take a look at this question, which is somehow close to yours.
Does the probability change if you know previous results?
If that's not what you are asking please provide us with more details.
answered 5 hours ago
Gâteau-Gallois
31319
add a comment |
up vote
1
down vote
Welcome to MSE,
it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more.
This is not true. If every choice of digits is independent, there is no change in the probabilities for the next digit of the sequence.
You can take a look at this question, which is somehow close to yours.
Does the probability change if you know previous results?
If that's not what you are asking please provide us with more details.
answered 5 hours ago
Gâteau-Gallois
31319
add a comment |
up vote
1
down vote
up vote
1
down vote
Welcome to MSE,
it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more.
This is not true. If every choice of digits is independent, there is no change in the probabilities for the next digit of the sequence.
You can take a look at this question, which is somehow close to yours.
Does the probability change if you know previous results?
If that's not what you are asking please provide us with more details.
answered 5 hours ago
Gâteau-Gallois
31319
Welcome to MSE,
it then implies that for the sequence to be random the probability of getting numbers greater than 5 is now more.
This is not true. If every choice of digits is independent, there is no change in the probabilities for the next digit of the sequence.
You can take a look at this question, which is somehow close to yours.
Does the probability change if you know previous results?
If that's not what you are asking please provide us with more details.
answered 5 hours ago
Gâteau-Gallois
31319
answered 5 hours ago
Gâteau-Gallois
31319
answered 5 hours ago
Gâteau-Gallois
31319
answered 5 hours ago
Gâteau-Gallois
31319
31319
add a comment |
add a comment |
mathaholic is a new contributor. Be nice, and check out our Code of Conduct.
mathaholic is a new contributor. Be nice, and check out our Code of Conduct.
mathaholic is a new contributor. Be nice, and check out our Code of Conduct.
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2
So, when you write, "integer", what you actually mean is "digit"?
– Gerry Myerson
5 hours ago