a set of distinct elements {x1, x2, x3.... , xn} . and you draw at random with replacement n elements samples, how many distinct elements samples can be created? example suppose you have {a,b,c} then sample with replacement = {a,a, a} , {a,a,b,}, {b,b,b}
Number of distinct elements in the set = n : (x1,x2,x3,...,xn)
you draw at random with replacement n elements
1st element in the sample can be any of the n elements (x1,x2,x3,..,xn):
2nd element in the sample can also be any of the n elements (x1,x2,x3,..,xn):
....
...
nth element in the sample can also be any of the n elements (x1,x2,x3,..,xn):
Number of distinct element samples that can be created = n x n x......n (n times) = nn
Number of distinct element samples that can be created = nn
For
three element {a,b,c} ; All possible 33 =27 distinct element samples are as follows
1 | a | a | a |
2 | a | a | b |
3 | a | a | c |
4 | a | b | a |
5 | a | b | b |
6 | a | b | c |
7 | a | c | a |
8 | a | c | b |
9 | a | c | c |
10 | b | a | a |
11 | b | a | b |
12 | b | a | c |
13 | b | b | a |
14 | b | b | b |
15 | b | b | c |
16 | b | c | a |
17 | b | c | b |
18 | b | c | c |
19 | c | a | a |
20 | c | a | b |
21 | c | a | c |
22 | c | b | a |
23 | c | b | b |
24 | c | b | c |
25 | c | c | a |
26 | c | c | b |
27 | c | c | c |
a set of distinct elements {x1, x2, x3.... , xn} . and you draw at random...
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