Veer Narmad South Gujarat University 2011-1st Year B.Com Mathemetics for Statistics, ,- , Veer Narmad South University - Question Paper
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University: Veer Narmad South Gujarat University
Program Name :First Year B.Com
Course Name: SB:0308 - Mathematics for Statistics, 1st Year B.Com Examination, March-2011, Veer Narmad South Gujarat University.
examination Month and Year: March-2011.
Duration : three hours
Maximum marks:- 70
Attachment :- PDF file containing SB:0308 - Mathematics for Statistics, March-2011.
SB-0308
First Year B. Com. Examination March / April - 2011 Mathematics for Statistics
Time : Hours] (0
[Total Marks :
N Seat No.:
6silq<3i Pi*unkil SnwiA u* <KH=fl. Fillup strictly the details of signs on your answer book.
Name of the Examination :
F. Y. B. Com.
Name of the Subject:
Mathematics for Statistics
|
-Subject Code No.: |
|
-Section No. (1,2......): Nil |
(0 faded VU(l *UH<UHl
Student's Signature
(3) wsO. "Hit'll y.-sj.'ii %iR d.
*1 -Mdl Jl*lHi WH 5HLHI :
lim
x>4
(0
x UcH. *iMd *l.
*1
*1
*1
*1
*1
(y) % <H HiUSt A *id B -(I Hl Ah *14
P(AnB) = x Ah dl x ?iWl.
(m) x Hia IR&d %&d E(x) = 2 *id
Yjx2-P(x) = 5 Ah dl V(x + 5) -(I &Hd tfltiL.
(e) <3. x Hia p(x=o)=g10 Ah dl n. *iWl.
(0) UlH&d x Hia lOid iii I P(x = ) = J/m U) % x:N( a2) Ah *id P{-6 <z <+b} = 0.8904 Ah dl b-tl &Hd
(fc) ML 7 + 11 + 15 + .........i 403 UH ?
(*10) Plg&iL (7, 2) ?Hd (3, 1)
*1
(*l) Bhd ?LlH\ :
(0
(0
+
+
x3-5x2+8x-4
-i.-i-
*->2 x -3x +4
l3+23+. I-9
w-oo i2+22+.
(H) (*l) % = x3 log Ah dl *iWl.
( 2 x +10
Ah dl ~r rfitfi.
(0 % y=
dx ) x=\
dx
U) (<l) 0*Hd %iM : jf3x2 +3X +e +
(0 &Hd ?LlH\ : j ( 2x + x2 - x3 )' dx
-1
H*l<U
Jl + X 1 (l) llm -r=-i=-
x>0 Jl + x ~
- Vi_x -1
2n + 3
-1
w-oo 4n + 5
(H) >' = 4x3-18x2+24x + llTfl *lfo$dH ?Hd -ddH &Hd
U) &Hd *iWl :
dx
(0 |(4 -2x)(4-3x)-t&
3 (*l) (*l) Bhd ?LlH\ : lim V2 + 3x V2i
x-0 4x
(0 % >,= Ah dl ~y
*
*
x dx
(3) J+Vx + ex + 5x3 j dx tj\_ SB-0308] 2
(h) &Hld* 43 + 53 + 63 +.....+ 203 Hi %R<UiL 3
U) oygO.TR mW.-i H yil ?Hd 7 H 29 d. dl d *teQ. 3
,. -yfx ~*J3
3 MM &Hd *M. : lim. Ir . *
x-3 yx + 1-2
(0 % = 23x+76lH dl rilNl. *
3
r (x-2)
(&{) i2 +32 +52 _|_........dl nMX US. (Idl *Rcilll S$L.
(h) HLd >Ll H 8 ?Hd 17 US. y dl 23 US. 3
(?H) Pi|9il A (5, 13) 5Hd B (1, 4)d mdL *HIH 2:3 IItRHL 3 [cHLd *di ftsdl HIH Hiql.
VO
(<h) Plg&iL (6, 4) ?Hd (2, l)d M 3
U) (<l) 4Rdl USl HWil : *
(a) HdWl.
(b) *Rc(l WHWdl.
(0 U[ct ?Hd uHl <H U Hia Ute Hia =>HIU 6. X
hM H* *Wl-fl i 3. H<-M H* Wl-d
1 s ,
WHWdl - . dl
(a) $5d <?f U*iS UH.
(*l) % <H Pl|*iL (a, -5) (2, a) 13 Ah dl
(H) 3x-5_y + 12 = 0 HIS Sll y-*Wl &d Pi|
U) (*l) WHlHdldl *RHllKl HHH lOid *l.
(0 % AB UWU fo.HRS *id OH:lH HSdMl Ah *14
*
X
*
e
10-P(A) = 3- p(b) = k Ah dl Kl &Hd tfltiL.
(*i) feul PUWSI WHlKl HdcH Mh <HHl. ddl LHhI H51 'SPillHl.
(h) HHld CHLUHL *UUl.
(h) ?HLHC-il Hlfedl HIS H*hM HlUC-t JilH Hh JIHldMl
&Hd HlHl :
|
xz |
0 |
1 |
2 |
3 |
|
) |
0.1 |
0.3 |
0.4 |
0.2 |
(*i) HM4 PUWSKI LHHl 'SPillHl.
*
X
(h) 9lU feul x HIS % n. = 5 *id P(x = 2): P(x=3) = 6:4 Ah dl *U PUWSI HIS H*H$ *id HHlfeld [toSH *M..
U)
?HLHC-i il*S HIS
(l) E(x-l)
(3) (x + 6) *id
|
2m x. |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
%i(HWHL/,(x.) |
0.1 |
K |
0.2 |
2 K |
0.3 |
K |
(*i) HHL'SH PUWSI WHlKl HdcH Mh WWl PUWSKI LHhI Wlicfl.
(<h) dlL ?HLHC-il Hlfedl HIS HLHd PUWSI Mh HlHl *id *iufetd [rBHl tfltiL. (e0-9 = 0.41 cil)
|
x: |
0 |
1 |
2 |
3 |
4 |
|
/: |
42 |
36 |
14 |
6 |
2 |
U) x:#(l50,400) A.H X
(i) p( 160 < x < Xj) = 0.2277
(ii) p(x<K2) = 0.0968 Ah dl K2-. &Hd ?LlH\.
e M *Wldd PUWSI Hia HHLdH HlHl Y
(H) Hi C-l x feH& &. %dl = 4d. Y 12-P(x = 0) = P(x = l) Ah dl PUWSI rflNl.
($) JUHISH fadHl 31% &Hdl 45 *di ?hM ?Hd 8% &Hdl Y 64 *di d. dl 5Hd HHlfeld faaUH 5>llHl.
Instructions : (1) As per the Instruction no. 1 of page no. 1.
(2) Statistical tables will be supplied on request.
(3) Figures to the right indicate full marks of the questions.
1 Answer the following questions :
(I) Evaluate :J - . 1
-(Vx-2)
x
_ 1
(2) If y~ . i- then find 1
5 Vx dx
1
(3) Find out the integration of -1/ with respect to x. 1
x '2
(4) If A and B are independent and equally likely events 1 and P(AnB)=x then find x.
(5) For a random variable x, in an usual notation E(x) = 2 1
and x2 -P(x)=5 then find V(x + 5).
(6) For a binomial variate x, if P(x = 0) = g10 then find n.. 1
(7) For the Poisson variate prove that P(*=0) = 1
(8) If a2) and P{-6 < z < +b} = 0.8904 then find the 1 value of b.
(9) Which term of the series 7 + 11 + 15 + .........is 403 ? 1
(10) Find the distance between the points (7, 2) and (3, 1). 1
lim
*->2 x -3x +4 .. I3 23 .........
(1)
+
(2)
2
2
2
2
2
2
2
4
2
2
2
2
2
~5-9-
00 12_|_22_|_.........
+
(b) (1) If y = x3 log then find
f 2 V
x +10
then find
dX )y =
X = 1
(c) (1) Evaluate : J f 3x2 +3X + e +
dx
V xy
(2) Evaluate : j" (2x + x2-x3)-
-l
2 (a) Evaluate
1 + x - 1
-v'-To /l+x -2 + 3 n
(1)
lim
(2)
-1
n-cc 4n + 5n
(b) Find maximum and minimum values of the function v = 4x3-18x2+24x+11-
(c) Evaluate :
2
(2) J (4-2x)(4-3x) t&
J2 + 3x -J2-5x
3 (a) (1) Evaluate : lim -
x>0 4x
logx d2y
(2) If y=3 ,then find
dx
(3) Evaluate : J (\--Jx + ex + 5x
dx
000
(b) Sum of the arithmetic series 4 +5 + 6 _
(c) The fourth term of the Geometic series is 7 and
7th term is 729 Find the series. 3
OR
(a) (1) Evaluate : j~f_2 2
(2) If v=23r+7Then find -7-. 2
J dx
f (*-2)
(3) Evaluate : J -~r dx . 2
(b) Sum the series i2+32+52 +........up to nth term. 3
(c) The third term of an arithmetic progression is 8 3
51
and the 17th term is Find the 23rd term.
2
(a) Find a point which divides the line joining A(5, 13) 3 and B(l,4)in the ratio 2:3.
(b) Find the equation of line joining points(6, 4) 3 and (2, 1).
(c) (1) Explain the following terms : 2
(a) F avourable events
(b) Conditional probability.
(2) A husband and wife appear in an interview for 4
two vacancies in the same post. The probability of
1
husband's selection is and that of wife's selection 1
is What is the probability that
(a) One of them will be selected,
(b) Neither of them will be selected ?
(a) If the distance between (a,-5) and (2,a) is 13 , then 3 find the value of a
(b) Find the slope and intercept on Y-axis of the line 3
3x-5_y + 12 = 0.
(c) (1) Prove the addition theorem of probability. 4
(2) If A and B are mutually exclusive and exhaustive
cases and 10.P(A)=3.P(B)=K then find K.
(a) Write the probablity density function of binomial 4
distribution. Also state its properties.
Define moment generating function.
Find the first four monents about mean from the following data :
(b)
(c)
|
xi |
0 |
1 |
2 |
3 |
|
p(*i) |
0.1 |
0.3 |
0.4 |
0.2 |
State the properties of poisson distribution
(a)
(b)
2
4
For a binomial variate x, if n=s and p(x=2) :p(x=3)=6:4
then obtain the mean and standard deviation for this
distribution.
Find :
(c)
6
(1) E(x-1)
(2) E(
x2 + 5)
(3) E[x+ 6) and
(4) V (x) for the following data :
|
Variate Xj |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
Probability P(xi) |
0.1 |
K |
0.2 |
2K |
0.3 |
K |
State the probability density function and properties of normal distribution.
Fit a Poisson distribution to the fallowing given
(a)
(b)
6
4
4
data and find expected frequencies : (
e 09 =0.4l)
|
x: |
0 |
1 |
2 |
3 |
4 |
|
/: |
42 |
36 |
14 |
6 |
2 |
If x:V(l50,400) and
(i) p( 160 < x < Kx) = 0.2277 and
(ii) P(x < K2) = 0.0968 then find the value of Kl an K2.
OR
Find moment generating function for discrete frequency distribution.
Random variate x follows binomial distribution with mean=4. If \2-P(x=0)=P(x = \), the find variance of it. In a normal distribution 31 % of the items are under 45 and 8% are over 64. Find the mean and standard deviation of normal distribution.
(c)
(a)
(b) (c)
6
4
4
SB-0308] 8 [ 300 ]
|
Attachment: |
| Earning: Approval pending. |
