Veer Narmad South Gujarat University 2011-1st Year B.A SB-0036 Statistics ( Higher ) ( 1 ) - Question Paper
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SB-0036
First Year B. A. Examination March / April - 2011 Statistics : Paper - I (Higher)
Hours] [Total Marks : 70
6silq<3i Puunkiufl [qaim SuwiA u* qsq Fillup strictly the details of signs on your answer book.
Name of the Examination :
F. Y. B. A
Name of the Subject:
STATISTICS : PAPER - 1 (HIGHER)
-Section No. (1,2......): Nil
(0 HHl V JWfL WftfHld d.
(3) ?HKiHU?L, etlSlilH *14 *UlilH fadcM Hl'RHlHl *U<l$L
(y) WiO. <H.l$ *UUC-U M& U&Vtl fc%|R d.
1 4Rdl U&ldl <3tR *UHl : 1Y
(*0 f(x) = 6x2 +9x-2 Ah dl /(3) /(2) &Hd
3 -30 r gHd
zr1 r+4
(3) % E(x) = 5, E(y) = 2 6lH dl E[2x + 3y] 41 &Hd
r3 _ Q
(y) &Hd HlHl lim -.
x2 x2
(m) Ptvk. H8dl4l cHLuHL &fed SlHWiL.
(?) WR xdl H3Wd*l *RHl d 6lH cHR *idfold HIS & Hfedl (3HHlL UH d ? t *iLHl.
(0) = 5x4 -4x3 + 8x2 + 4x + 3 x H.cH OlMd *Rl.
* (?h) (3HH>Ll &fed H
(h) Mh x = 50 + P-P2 Hia P= 1, 2, 3, 4, 5, 6, 7. M
5Hl<HH l1l.
U) Mh D = 50-7t/P Hia P= 4, 9, 16, 25. D 41 Y
&Hd Hiql.
*WU
* (*l) ouIMh 5HU$tl4l <*HU ?HlHl. <>iIMh HUStK ?HLHR i H
Hiql.
(<h) 4R41 Hlfe4l4l (3HH>L M ?Hd Hiql : H
|
X |
0 |
1 |
2 |
3 |
4 |
|
P(x) |
1 |
4 |
6 |
4 |
1 |
|
16 |
16 |
16 |
16 |
16 |
(b) ?HdRHdd MMK (3LldL Hldl UfrillHl Hia <H UIH UHLdl Hiql.
3 (?h) llHl> lim lim 41 *i[ anwiL.
a: *0 xoo xoo
(h) 141 x +3 41 Bnd Hiql.
x*1
U) Bnd Hiql.
f 5
(*l) faMddl (3UH>ll WWl. PlSH HIS oy8UR ?Hd
<HlllRdl GHHHl GU6*5l &fed tt*m<il.
(H) % Mh /(x) aiL x *UU$t faMd $l
f'(x)= lim X + filH dl dd\ (3HHl3L M
/iO h
fix) = 8x + 5 fa.&<3.d 3RI.
(h) Hll-iL fok'ti.'i X UcH [ciMd
(*0 f(x) = (x2 + x)(2x + 3)
(0 f(x) = (x2 +x + 2)|(x + 9)
M IR&d dHL lOid
7i = n(n l)(n 2)......(n r + 1)
Pr
(<h) 7 Hl ?Hd 3 iOllxtHLafl. -HSL HSL
%HL ?HLWLHL ?hM 2 4 fl.fo.Rl kefl. &d UttS. M
?1IH ?
(h) M H>SL 5HM =lHd d q.U3.lH ?H *Rd
1, 3, 5, 7, 9 Hl*(l aiR ?HLL4l keft fll Hdlcfl. %1IH ? *U*M keft fll 5,000 *di *M 6$l ?
*WU
(*l) *ufa%ld *kz& % ? *ufa%ld HlMl d-ft U<SiRt %LH*M.cCl.
(h) 4Rdl HVtt 1998 dl v{ Hia &Hd ?HHLd #t.
|
|
1988 |
1992 |
1996 |
2000 |
2004 |
|
&Hd |
25 |
30 |
40 |
55 |
60 |
(*l) % A ?Hd B UU foq.R$ H2dl*it <lH dl Kiteld fldHl fllfad b$L I P(A + B) = P(A) + P(B).
(<h) eEdd <H dlM HIS (3H&<U& HtHL=(l. *11 <Hd dlM*ll H HqciciLl ICHLciHl cbt *14 d *ld
j/ &. <HHHL(l *il9lHl *M HIM WHlHl kefl. ?
U) 5H Mni 5 efl&l *ld 7 lll 41 &. dHL(l 2 41 *{Z* &d Y <H<UH'l ?Hiq. dl d C-ftc-lL *id iLL Vudl WHlHl kefl. ?
H*l<U
H (*i) *Rc(l (HL=ldL4l <*HU *M IR&d %&dHL lOid M H
D,./D> P(AnB)
P(A/B)= WL p(5)>0.
(<h) &d 4lHC-iL 52 UTtWl 2 HtIL &d <H<UH'l H
*Uq. &. *11 H-di <H <>U*ll6 *mi <H .L'iCl <t<u4l WHlHl *M..
U) (HL=ldL4l <*HU *M d4l HHl WWl. Y
ENGLISH VERSION
Instructions : (1) As per the instruction no. 1 of page no. 1.
(2) Answer all questions.
(3) Figures to the right indicate full marks of the question.
(4) Graph papers, logarithmic table and statistical table will be supplied on request.
1 Answer the following questions : 14
(i) If f(x) = 6x2 + 9x - 2 then find the value of /(3) /(2).
(ii) Find the value of r if c9 , .
v / zrl r+4
(iii) If E(x) = 5 and E(y) = 2 then find E[2x + 3,y].
X O
(iv) Obtain the value of lim -.
x2 x 2
(v) Define Independent events with suitable example.
(vi) Which method of interpolation is used when intervals of x are not equal ? Give its formula.
(vii) Differentiate with respact to x
y = 5x4 4x3 + 8x2 + 4x + 3
Explain the uses of function in economics. 5
Draw the graph of the function = 50 + P P2
Define Mathematical expectation. Derive the formula 5
of 12 with the help of mathematical expectation.
Find mean and variance from the following 5
information.
|
X |
0 |
1 |
2 |
3 |
4 |
|
P(x) |
1 |
4 |
6 |
4 |
1 |
|
16 |
16 |
16 |
16 |
16 |
(c) An unbiased die is tossed. Find first two raw 4
moments for all possible outcomes.
3 (a) . Explain its meanings. 5
v 7 a: *0 xoo xoo
(b) Obtain the value of x +3 using table. 5
a:>1
(i) lim -
,. 4x + 6x + 4
(ii) lim 5-
xoo 2x + 3x 5
OR
Explain the uses of differentiation in economics. Explain multiplication and division law for differentiation with suitable examples.
3 (a) (b)
(c)
4 (a) (b) (c)
If the differentiation of the function f(x) with
. tu V f(x + h)-f(x) , respect to x is / W i1 --- then using
this result find the differentiation of f(x) = 8x + 5.
Find the differentiation of the following functions with respect to x.
(i) f(x) = (x2 + x)(2x + 3)
(ii) f(x) = (x2 + x + 2)\(x + 9)
In usual notation prove that 5
n =n(n l)(n 2)......(n r + 1)
Pr
In a committee of 7 males and 3 females, in how 5
many ways a sub committee of 3 can be chosen in such a way that it consists at least 2 females.
No digits being used more than once in each number, 4 how many integer number of four digits can be formed using 1, 3, 5, 7, 9 digits. Out of them how many numbers are more than 5000.
(a) What is interpolation ? Explain Newton's method
for interpolation
(b) Estimate the value of price for the year 1998 from the following table :
|
Year |
1988 |
1992 |
1996 |
2000 |
2004 |
|
Pr ice |
25 |
30 |
40 |
55 |
60 |
(a) In usual notations if A and B are mutally exclusive events then prove that P(A +B) = P(A) +P(B).
(b) A man applied for two jobs. The probabilities of getting jobs are independent of each other and are Y2
and J/g respectively. What is the probability that he gets at least one of them ?
In a bag, there are 5 green and 7 black balls. Two balls are drawn at random, what is the probability that one is green and other is black.
OR
Define conditional probability. In usual notation
D,./D> P(AnB) prove that *\A IB) pg > where P(B) > 0 .
Two cards are randomly drawn from the well shuffled pack of 52 cards. What is the probability that these selected two cards are either two kings or two queens. Define mathematical definition of probability; also state its limitations.
SB-0036] 7 [400]
1
WU
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