RTU 2016 Question Paper Semester IV Computer Science and Engineering Statics and Probability Theory

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RollNo. Total No ot Pages: I
N 4F4162
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t{ B.Tech. IV-Sem (Nlain & Back) Exam; June-July 2016
$ Computer Science & Engineering
ET
$ 4CS3A Statistics & Probability Theory
Common with CS, IT

Time: 3 Hours Maximum Marks: 80
Min. Passing Marks (Main & Back): 26
Min. Passing Marks (OId Back): 24
Instractions to Candidate s : -

Attempt any five questions, selecting one question from each unit. All
Questions carry equal marks. Schematic diagrams must be shown
wherever necessary. Any .data you feel missing suitably be assumed and
stated clearly.
Units of quantities used./ calculated must be stated clearly.
(Ise of following supporting material is permitted during examination.
(Mentioned in form No.205 )

1. Normal distribution Table 2. Scientific calculator

UNIT.I
Q.1 (a) A bag has 4 white and 3 black balls while another bag has 3 white and 5 black
balls. A ball is drawn from the first bag and without noting its colour, is put into
the second bag. Then a ball is drawn from the second bag. Find the probability
that it is white. t8l
(b) The chance that a doctor will diagnose a disease correctly is707o. The chances of
death of patient after correct diagnosis is 357o while after wrong diagnosis it
80%o.If a patient dies after taking his treatment, find the probability that he was
diagnosed. t8l
(i) Wrongly
(ii) Correctly

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- (a)
Q.t \-/ Find the rlrna^-r q
r'n"tio, random variabre
X whose p.m.r. i,
ff:T=;;:-'eraling
."''i'i X = 0' 7'
8
(b) Thirt"",cards 2,3 and then
fin< lt and
are drawn si , ":u 1t
,, "

.*0. td and from ^* "
othl; r."Iillln1ou-slr
rh. 1s1d):^1:h
score orthe r3;roins ro their.";#flIL;lrr?;J?J::::::1,
"

---^* urv expectation
#of
e.z @) Find mean & rro*i^.^ uNrT-[
-
(b) ffi',:l*ifrffiilfioi1son distriu,,ion
factory i. ,r""]- ":"^l'":' The distribution of u

il-"r::f*t*r:'.#rJ*;*;-i:-#l,H;'""tr??:ffi:'ii
(i, Less than t45 tsl

Q.z (a) Find the mean
and .,--,
q
rlance of normal
(b) distribution.
lhe foilowing data the number l8l
rirter ror r;
;:, ;:1:l"i'
:eds' Fit q ;f.1eeds
urlrultu&l dist
germinating
out of 10 on damp
f---------- ";;;'*r, 'to this data.

;' :,j _12 8 6 0 t8j

0 0 0 0
Q.3 @) Find the corr^ror;^-
correlation
UNIrT-[r
coefficie
rhar: 1
= 15, rx = 50, ,,
*T, ir
is given:
(b) Ten competitt . ' -r = ;:::|_Til :j
- --7u: Lx- - 290,
Ly2 = 300,
- --'|rs m a beauty xxy = -115.
order. contest are ranked
by three judges
Isl
in the forowing
Judge I

Iudge2la5lo 2 4 g 7 8
3 s 8 43
4 7 10 2 1
Judge, 6 4 g ^ 8 t a g
userherankcr
^: 2 3 lo 5 7
lation coefficient
nearest approach to discuss which
which
to common pair of judges
,"r,",r"rjlull""t have rhe
[484162] l8l
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[82ool

OR
Q.3 (a) Fit a parabola of second degree, taking x as an independent variable to the
' following data.
x 1.0 1.5 2.0 2.5 3.0 3.5 4.0
y 1.1 1.3 t.6 2.6 2.1 3.4 4.1 t8l
(b) Find the two lines of regression and coefficient of correlation for the data given
below.
n = 18, Lx =l2,Iy = 18. Ex2 = 60. Ly2 = 96, Ixy
= 49. t8t
UNIT.IV
Q'4 (a) Customers arrive aL a box office with one ticket window according to a poisson
input process with mean rate of 30 per hour. The time required to serve a
customer has an exponential dist'with mean 90 seconds. Find
(i) Average line length
(ii) Average queue length
(iiit Average waiting time in queue
(iv) Average time spent by a customer in the system
t8l
(b) If for a period of 2 hours in a day, customers arrive in a barber's shop that has a
space to accommodate only 4 customers. Arrival rate of customers
is 3 per hour
and service time is 36 minutes per customer. Find for the above period.
(i) The probability that there is no customer in the shop.
(ii) Average number of customers in the shop.
tgl
OR
Q'4 (a) A petrol pump has 2 pumps- The service time follows the exponential
distribution with a mean of 4 minutes and vehicles arrive for service in poisson
fashion at the rate of l0 per hour. Find
tgl
(i) The probability that an anival of a vehicle would have to wait.
(ii) The expected percentage of idle time for each pump.
(b) In a shop there are two computers for carrying out the job work. The average
time per job on each computer is 20 minutes per job and the average arrival
raie
is 2 jobs per hour. Assume the job times to be distributed exponentially. If the
maximum number ofjobs accepted on a day be 6, then find
t8t

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(i) The expected number of jobs waiting for computer'
(ii) The total time lost Per daY'
UNIT-V
birth death process. t8]
Q.s (a) write a short note on discrete parameter
(b) Three advo.u.", e,
g, c' n*" at t = 0; 450, 500, 600 clients respectively. During

oneyearthoughnonewclienthasbeenadded,migrationsfromonetotheother
t8l
have taken Place as follows:
From A 50 have gone to B and 25 to C

From B 50 have gone to A and 100 to C

c z1have gone to A
. From
assocliated
Prepare the transition probability
matrix and find the number of clients
with A, B, C after one Year'
OR

transition probability is given by
Q.5(a)Amanwhilegoingtoofficeheuseseitherofthetwomodesoftransportationt8l
either a clty bus or his scooter. The
I uu' stoott' I
- Busl o I
ttz ttz ]
I
P
scooter I

TheinitialStateofprobabilitydistributioni.e.onfirstdayis
ts t-l
p 1r ) =[i, 6.l

Find
(i) The probability that he takes a bus on the third day'
(ii) The probability that he goes by scooter in the long run'
(b)Ahousewifebuysthreekindsofcereals:A,B,C'sheneverbuysthesame
cerealsonsuccessiveweeks.IfshebuyscerealsA,thenthenextweekshebuys
cerealB.However,ifshebuysBorC,thenthenextweeksheisthreetimesas
.likelytobuyAastotheotherbrand.Findthetransitionprobabilitymatrix't8]

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