Assume that (Ai , Bi) for I = 1, 2, . . . , n is a succession of free and indistinguishably dispersed 2-layered irregular factors where Ai and Bi are autonomous with minor disseminations Ai ∼ U[α, β] and Bi ∼ U[0, γ] for every I = 1, 2, . . . , n. (I) Define irregular factors Ii for I = 1, 2, . . . , n to such an extent that Ii = ( 1 if Bi ≤ AifX(Ai) 0 in any case and sd that Var(Zn) ≤ 1 4n . [5 marks] (ii) Using Chebyshev's imbalance show that Zn merges in likelihood to the savage irregular variable with esteem µ/(γ(β − α)). [5 marks] (iii) Describe a calculation to assess the mean µ of the arbitrary variable X. You might accept with the end goal of your calculation that you have a capacity that profits irregular places of the given structure (Ai , Bi). [5 marks]

Depict an O(n log(n)) calculation in view of a variety of union sort to fifind the

nearest sets of a given arrangement of focuses lying in a plane. You might expect to be that the set

of focuses is given as a connected rundown of (x, y) organizes. [8 marks]

Cautiously demonstrate that your calculation can never take more time than O(n log(n)).

[6 marks]

Change, with clarification, your calculation to fifind the sets of focuses with least

Manhattan distance. The Manhattan distance between focuses (x1, y1) and (x2, y2)

is |x1 − x2| + |y1 − y2|. [6 marks]

1

[TURN OVERCST.2000.6.2

2 Computer Design

For what reason are the accompanying assertions misrepresentations?

(a) MIPS is a precise measure for looking at execution among PCs.

[5 marks]

(b) A benchmark is a normal program which precisely predicts the presentation

of any remaining applications. [5 marks]

(c) Complex guidance set PCs limit the semantic hole between

machine code and significant level dialects, in this manner making applications run more

rapidly. [5 marks]

(d) Data stores generally further develop processor throughput. [5 marks]

3 Digital Communication I

Look at circuit exchanging and bundle exchanging, focusing on channel

qualities and asset effiffifficiency. [7 marks]

What is wave division multiplexing (WDM)? Is it more like circuit exchanging or

bundle exchanging and why? [7 marks]

Frequency change is the cycle, either optical or optical-electronic-optical,

of getting a sign on one frequency and sending on another.

How waves length transformation facilitate the issue of steering optical transporters in a

network? [3 marks]

"The tremendous limit of WDM frameworks will imply that IP becomes repetitive."

Examine. [3 marks]

2CST.2000.6.3

4 Computer Graphics and Image Processing

Give a calculation for drawing the piece of a circle which lies in the fifirst octant.

Accept that the circle has number range and is focused at the beginning. Accept

that you have a capacity setpixel(x, y) which turns on pixel (x, y). [10 marks]

Determine a lattice, or a result of networks, to play out a clockwise 2D turn of

erratic point, θ, about an inconsistent point, (xc, yc). [4 marks]

Give a calculation to learn whether the Bezier bend defifined by P1P2P3P4

exists in some resistance, , of the straight line portion, P1P4, which joins the

Bezier bend's end focuses. Your calculation should return bogus assuming the Bezier bend is

outside the resilience; it should return valid assuming the bend is well inside the resistance;

it might return either evident or bogus on the off chance that the bend is inside, yet all the same not great inside, the

resilience. [6 marks]

Segment B

5 Comparative Programming Languages

Give a concise outline of the super syntactic develops found in the programming

language Smalltalk. Different dialects frequently have the restrictive develops

in the event that else and keeping in mind that. Show how these two builds can be defifined in Smalltalk.

[8 marks]

Outline the utilization of Smalltalk by showing how you would defifine a technique to

register the factorial of a number. [8 marks]

In spite of the fact that Smalltalk was initially intended to be an interpretive language, present day

executions are decisively more effiffifficient. Brieflfly frame what procedures

could have been utilized to make this improvement. [4 marks]

3

[TURN OVERCST.2000.6.4

6 Compiler Construction

Depict how a parse tree can be converted into a succession of low level computing construct

directions in light of an example matching chart got from a bunch of tree modifying

rules where each standard has an expense and a relating section of code. Show

your response utilizing the accompanying guidelines:

Ri = Kk LDI Ri,Kk Cost 2

Ri = add(Ri,Kk) ADDI Ri,Kk Cost 3

Ri = add(Ri,Rj) ADD Ri,Rj Cost 3