Question

3. Consider the following Matlab code. s-0; clear s.norm for i 1:10000 r-rand(1); % generate a uniform random, number on [0,1] S-S+(3+rr) s.norm(i)-S/i end plot( 1:10000,s.norm) % make a plot of s.norma) versus i (5 pts) What will the plot look like? (10 pts) Will the function/vector s.norm(n) converge to something as n gets large? If so, what? If not, why not? Justify your answer. (5 pts) If we were to run this code multiple times - overlaying the plots on top of each other (with hold on, for example) - what will the plots look like?

Answer 1

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AS FOR GIVEN DATA,,

Consider the following Matlab code. clear s.norm for i-1:10000 r-rand(1); % generate a uniform random number on [0,1] s.norm(i)-s/i end plot( 1:10000,s.norm) % make a plot of s.norm(i) versus i (5 pts) What will the plot look like? (10 pts) Will the function/vector s.norm(n) converge to something as n gets large? If so, what? If not, why not? Justify your answer (5 pts) If we were to run this code multiple times - overlaying the plots on top of each other (with hold on, for example) - what will the plots look like?

EXPLANATION ::-

What will plot look like?

Initially plot will fluctuate between 3 to 4 and the gradually move towards 3.3333333

3.5 3.45 3.4 3.35 3.3 3.25 3.2 3.15 3.1 2000 4000 6000 8000 10000

Will function converge to something if n gets large?

Yes in each loop s is incremented by 3 in each loop and r is random is variable between 0 and 1, r*r is added in each loop

taking average value r*r =
.3-3 0
= 1/3 - 0/3 = 1/3

So for any n s_norm(n) =
3 *n1/3*n
= 3.333333333

Multiple runs how would plot look like?

3.9 3.8 3.7 3.6 3.5 3.4 3.2 1000 2000 4000 5000 6000 7000 8000 9000
Function takes almost every value between 3 and 4 for n = 1 and gradually converge to 3.33333333 as number of iteration(n) increases.

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