Which of the following best describes the term constructions in geometry?
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The expected length of code for one encoded symbol is
where is the probability of picking the letter
, and
is the length of code needed to encode
.
is given to us, and we have
so that we expect a contribution of
bits to the code per encoded letter. For a string of length , we would then expect
.
By definition of variance, we have
For a string consisting of one letter, we have
so that the variance for the length such a string is
"squared" bits per encoded letter. For a string of length , we would get
.
Odd numbers take the form , where
is an integer. When
, the last odd number would be 799. So we're adding
By reversing the order of terms, we have
and we can pair up terms in both sums at the same position to write
so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:
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We could also make use of the formulas,
We have