Expectation to draw all numbers from 1 to 100
$begingroup$
I have 100 papers each contains numbers like
(1,2), (2,3),(3,4),..., (99,100), (100,100). I draw
each paper and note down its numbers and return that paper.
How any times I have to draw on average to note down all
numbers from 1,2, .., 100?
Let $X_n$ be the total numbers on average drawn at $n$-time.
I observed experimentally $X_{n+1}$ is around $X_n+(1-frac{X_n}{100})2$
expected-value
asked Dec 29 '18 at 10:53
strstr
425
$endgroup$
add a comment |
$begingroup$
I have 100 papers each contains numbers like
(1,2), (2,3),(3,4),..., (99,100), (100,100). I draw
each paper and note down its numbers and return that paper.
How any times I have to draw on average to note down all
numbers from 1,2, .., 100?
Let $X_n$ be the total numbers on average drawn at $n$-time.
I observed experimentally $X_{n+1}$ is around $X_n+(1-frac{X_n}{100})2$
expected-value
asked Dec 29 '18 at 10:53
strstr
425
$endgroup$
$begingroup$
Do papers contain different numbers, or also twice the same number?
$endgroup$
– Did
Dec 29 '18 at 11:57
$begingroup$
Papers contain all different consecutive numbers except last paper which contains (100,100).
$endgroup$
– str
Dec 29 '18 at 12:28
add a comment |
$begingroup$
I have 100 papers each contains numbers like
(1,2), (2,3),(3,4),..., (99,100), (100,100). I draw
each paper and note down its numbers and return that paper.
How any times I have to draw on average to note down all
numbers from 1,2, .., 100?
Let $X_n$ be the total numbers on average drawn at $n$-time.
I observed experimentally $X_{n+1}$ is around $X_n+(1-frac{X_n}{100})2$
expected-value
asked Dec 29 '18 at 10:53
strstr
425
$endgroup$
I have 100 papers each contains numbers like
(1,2), (2,3),(3,4),..., (99,100), (100,100). I draw
each paper and note down its numbers and return that paper.
How any times I have to draw on average to note down all
numbers from 1,2, .., 100?
Let $X_n$ be the total numbers on average drawn at $n$-time.
I observed experimentally $X_{n+1}$ is around $X_n+(1-frac{X_n}{100})2$
expected-value
expected-value
asked Dec 29 '18 at 10:53
strstr
425
asked Dec 29 '18 at 10:53
strstr
425
edited Dec 29 '18 at 11:01
str
asked Dec 29 '18 at 10:53
strstr
425
asked Dec 29 '18 at 10:53
strstr
425
asked Dec 29 '18 at 10:53
strstr
425
425
$begingroup$
Do papers contain different numbers, or also twice the same number?
$endgroup$
– Did
Dec 29 '18 at 11:57
$begingroup$
Papers contain all different consecutive numbers except last paper which contains (100,100).
$endgroup$
– str
Dec 29 '18 at 12:28
add a comment |
$begingroup$
Do papers contain different numbers, or also twice the same number?
$endgroup$
– Did
Dec 29 '18 at 11:57
$begingroup$
Papers contain all different consecutive numbers except last paper which contains (100,100).
$endgroup$
– str
Dec 29 '18 at 12:28
$begingroup$
Do papers contain different numbers, or also twice the same number?
$endgroup$
– Did
Dec 29 '18 at 11:57
$begingroup$
Do papers contain different numbers, or also twice the same number?
$endgroup$
– Did
Dec 29 '18 at 11:57
$begingroup$
Papers contain all different consecutive numbers except last paper which contains (100,100).
$endgroup$
– str
Dec 29 '18 at 12:28
$begingroup$
Papers contain all different consecutive numbers except last paper which contains (100,100).
$endgroup$
– str
Dec 29 '18 at 12:28
add a comment |
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$begingroup$
Do papers contain different numbers, or also twice the same number?
$endgroup$
– Did
Dec 29 '18 at 11:57
$begingroup$
Papers contain all different consecutive numbers except last paper which contains (100,100).
$endgroup$
– str
Dec 29 '18 at 12:28