This paper concentrates on the primary theme of BEFORE GETTING TO THE QUESTION, WE NEED SOME OBSERVATIONS. (I) RECALL THE FORMULA FOR THE SUM OF… in which you have to explain and evaluate its intricate aspects in detail. In addition to this, this paper has been reviewed and purchased by most of the students hence; it has been rated 4.8 points on the scale of 5 points. Besides, the price of this paper starts from £ 40. For more details and full access to the paper, please refer to the site.

Before getting to the question, we need some observations.

(i) Recall the formula for the sum of a geometric series:

(1−ρ)−1, for |ρ|

(ii) Differentiating both sides of the equation in (i) with respect to ρ, we (iii) If a symbol s from a perfect zeroth-order source occurs in the source text (randomly and independently of all other occurrences) with relative frequency f , then, starting from any point in the source text and going either forward or backward, assuming the source text extends infinitely in both directions, the probability of reading through exactly k letters before coming to the first occurrence of s (at the (k +1)st place scanned) is

using (ii). To put it another way, s occurs on average once every 1/f letters, which agrees with intuition, since is the relative frequency of s.)

(iv) Suppose that S = {s1,…,sm } is the alphabet of a perfect zeroth-order source, with sj having relative frequency j , 1 ≤ j ≤ m. Suppose the source text is encoded by the interval method, using some prefix-free set C = {ω,ω1,…} of code words. Then the average length of a code word Replacing sj will be so the average length of a code word replacing a source letter will be

Finally, the problem. Show that for any zeroth-order source, in interval encoding using C = {0,10,110,···}, the average length of a code word replacing a source letter will be m = |S|.