MSO201A/trSO 2O9: ProbabilitY and 2OL2-2OL3: II Semester Quiz II Tirne Aliowed: 30 Minutes Statistics Maximum Marks: 20 Name: Roll No.: 1. Let X be a random variabie with moment generating function 1 i , 11 , Mx(t): G + :u-i + iu',, € R. (i) Find P(2x2 - x - r:0); (ii) Calculate E(X); (iii) Calculate E(X2). 2. Let Z - N (0,1) and let h : -+ IR be definecl by : max(r, 0), 2 e R.. Find the Eo M*dl ariance of h.(Z). 56L"'- t (a) | iE *l* ?n( U-,* t -- Lc qv , tt - 7€ I e", LgrR 3 rlar'Lu a6r*, p(zxL-x-t=o) = ?(Ox+l(x-rl =o) m& 4 ^fanJrn Vtu>iab)2. X ol.o"sc is ff*" bJ ?(x=-+ d x=t)- 7(x---+)+?(x=t) I , L7 _ -,1- _ Lt i"6 E L6 2 HarK; L na^K x o L L 1- {*k) L 16 L \ -L L6
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MSO201A/trSO 2O9: ProbabilitY and2OL2-2OL3: II Semester
Quiz IITirne Aliowed: 30 Minutes
Statistics
Maximum Marks: 20
Name:
Roll No.:
1. Let X be a random variabie with moment generating function1 i , 11 ,Mx(t): G + :u-i + iu',, R.
(i) Find P(2x2 -
x -
r:0);(ii) Calculate E(X);(iii) Calculate E(X2).
2. Let Z -
N (0,1) and let h : R -+ IR be definecl by h(r) : max(r, 0), 2 e R.. Find theEo M*dlvariance of h.(Z).
56L"'- t (a) |
iE *l*?n(
U-,*tI
--Lcqv , ttt- 7I
e", LgrR
3 rlar'Lua6r*, p(zxL-x-t=o)
= ?(Ox+l(x-rl =o)
m&! 4 ^fanJrn Vtu>iab)2. X ol.o"scis ff*" bJ
?(x=-+ d x=t)-7(x---+)+?(x=t)I , L7
_
-,1- _Lt i"6EL6
2 HarK;
L na^K
x o LL 1-{*k) L16 L\ -LL6
-
0x+ -+tL + txL16 Z' L, ' G' TcI , llI tL
Ll(
(6) Lg) =
Mh".a (x)
rlJ t=o
l* ",t*f r=of t -Ll,rt d''' *+ e! + Jl-B l(
Ll6
o"x f^ + t+)'L+LIL I C3T
JIIC
xLt1
f*FTxrtlo=,[+ "\ + +i .*] L=o
E (x') =(c) tlr'x
AIkr,E (x")
=
1, , ll-
T[( I(3LT
2 tlaat.-,
-
So{.": 2:
E (uL'))Vott (trt )) = E(hb))'_= t (yn^x (=,0 ))
= i*o, (b,o) t 7"/,-a Jzr(* z ev"l-Ag=\'o -EA
4t(LJfi Jo-
I
r--J zx
(e thb)) )"
^>
C (he))' = =(rnor
(z,o) )'= \U^x(z,o))" h r*/'rb
-6"O
- f -t-"
-1.-)6^D
I
GI
-
--.
JfrL
qL
-bl-,e. '- d>
I]*"' e L 'LL
2 tlr*rtli">
2nanl6
7 narr K;
L lMo.rt{>
lsl-lz
L
T-IzT
2 Ylanka
Var'(nt,)) = r r 12\c^l
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