Assignment Questions BITS

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BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

HYDERABAD CAMPUS SECOND SEMESTER 2015-2016

MATH F113: PROBABILITY AND STATISTICS: ASSIGNMENT- 1.

NAME: ID:

Q.No 1 2 3 4 5 6 7 8 9 10

Page

NO:

INSTRUCTIONS TO STUDENTS

1. Submit your own assignment on 11th March 2016 at 8.00 A.M uring test!1 "a"er istribution by

showing your #$ car. La! "#$%&""&'(" a)! (' a**'+! Ca)) 0

%a)/".

2. Assignment shou% be neat%y hanwritten on A& si'e white sheets ()oth sies can be use*.

DO NOT SUBMIT YOUR ASSIGNMENT IN FOLDER.+. Photoco"ies o, assignments wi%% not be acce"te.&. -io%ation o, any instruction s"eci,ie aboe wi%% resu%t ERO mar/s in your assignment.

Answer a%% uestions. O(! #!"&'( +&** $! 4'"!( a )a('% ') !a*#a&'(.





MATH F113: PROBABILITY AND STATISTICS

ASSIGNMENT- 1

Q1. A subect is a%%owe a seuence o, g%im"ses to etect a target. et

Gi={the target isdetected onthei thglimpse } with

G

¿ P(¿¿ i) pi ¿

. Su""ose the Gi'

s are ine"enent eents

an write an e4"ression ,or the "robabi%ity that the target has been etecte by the en o, the nth g%im"se.

Q.2 A system consists o, two com"onents. 5he "robabi%ity that the secon com"onent ,unctions in a satis,actory

manner uring its esign %i,e is .3 the "robabi%ity that at %east one o, the two com"onents oes so is .63 an the "robabi%ity that both com"onents o so is .7. 9ien that the ,irst com"onent ,unctions in a satis,actory manner

throughout its esign %i,e3 what is the "robabi%ity that the secon one oes a%so

Q+. A transmitter is sening a message by using a binary coe3 name%y3 a seuence o, 0;s an 1;s. <ach

transmitte bit (0 or 1* must "ass through three re%ays to reach the receier. At each re%ay3 the "robabi%ity is .20that the bit sent wi%% be i,,erent ,rom the bit receie (a reersa%*. Assume that the re%ays o"erate ine"enent%y

o, one another. 5ransmitter → =e%ay 1 → =e%ay 2 → =e%ay + → =eceier

a. #, a 1 is sent ,rom the transmitter3 what is the "robabi%ity that a 1 is sent by a%% three re%ays b. #, a 1 is sent ,rom the transmitter3 what is the "robabi%ity that a 1 is receie by the receier

&. 5he %ength o, human "regnancies ,rom conce"tion to birth a""ro4imates a norma% istribution with a mean o,

266 ays an a stanar eiation o, 16 ays. >hat "ro"ortion o, a%% "regnancies wi%% %ast between 2&0 an 270

ays (rough%y between 8 an months* >hat %ength o, time mar/s the shortest 70? o, a%% "regnancies

. Assuming that the iameters o, 1000 brass "%ugs ta/en consecutie%y ,rom a machine ,orm a norma%

istribution with mean 0.71 cm an stanar eiation 0.0020 cm3 how many o, the "%ugs are %i/e%y to be

reecte i, the a""roe iameter is [email protected]& cm

6. onsier a iscrete ranom ariab%e B with a "robabi%ity ,unction

( ) ( )

11 2

1

0 Otherwise

, x , ,... x x p x

,

= +=

Cin <(4* an M9C (i, e4ists*.



7. One sate%%ite is scheu%e to be %aunche ,rom a"e anaera% in C%oria3 an another %aunching is scheu%e

,or -anenberg Air Corce )ase in a%i,ornia. et A enote the eent that the -anenberg %aunch goes o,, onscheu%e3 an %et B re"resent the eent that the a"e anaera% %aunch goes o,, on scheu%e. #, A an B are

ine"enent eents with P ( A* D P ( B*3 P ( A∩B* E 0.1&& an P ( AUB* E 0.626. $etermine the a%ues o, P ( A* an

P ( B*.

8. A "ersonne% manager is to interiew ,our caniates ,or a ob. 5hese are ran/e 13 23 +3 an & in orer o, "re,erence an wi%% be interiewe in ranom orer. Foweer3 at the conc%usion o, each interiew3 the manager

wi%% /now on%y how the current caniate com"ares to those "reious%y interiewe. Cor e4am"%e3 the interiew

orer +3 &3 13 2 generates no in,ormation a,ter the ,irst interiew3 shows that the secon caniate is worse thanthe ,irst3 an that the thir is better than the ,irst two. Foweer3 the orer +3 &3 23 1 wou% generate the same

in,ormation a,ter each o, the ,irst three interiews. 5he manager wants to hire the best caniate but must ma/e

an irreocab%e hireGno hire ecision a,ter each interiew. onsier the ,o%%owing strategy: Automatica%%y reectthe ,irst s caniates an then hire the ,irst subseuent caniate who is best among those a%reay interiewe

(i, no such caniate a""ears3 the %ast one interiewe is hire*.

Cor e4am"%e3 with sE23 the orer +3 &3 13 2 wou% resu%t in the best being hire3 whereas the orer +3 13 23 &wou% not. O, the ,our "ossib%e s a%ues (03 13 23 an +*3 which one ma4imi'es P (best is hire* H Hint: >rite out

the 2& eua%%y %i/e%y interiew orerings sE0: means that the ,irst caniate is automatica%%y hire.I

. $e,ine ensity ,unction ,or >eibu%% istribution then ,in mean3 ariance3 stanar eiation3 momentgenerating ,unction o, the istribution ( i, e4ists* an mention at%east two rea% time a""%ications.

10. $e,ine ensity ,unction ,or )eta istribution then ,in mean3 ariance an stanar eiation3 momentgenerating ,unction o, the istribution ( i, e4ists* an mention at%east two rea% time a""%ications.





MATH F113: PROBABILITY AND STATISTICS: ASSIGNMENT- 1.

NAME: ID:

Q.No 1 2 3 4 5 6 7 8 9 10

Page

NO:

INSTRUCTIONS TO STUDENTS

. Submit your own assignment on 11th March 2016 at 8.00 A.M uring test!1 "a"er istribution by

showing your #$ car. La! "#$%&""&'(" a)! (' a**'+! Ca)) 0

%a)/".

6. Assignment shou% be neat%y hanwritten on A& si'e white sheets ()oth sies can be use*.

DO NOT SUBMIT YOUR ASSIGNMENT IN FOLDER.7. Photoco"ies o, assignments wi%% not be acce"te.

8. -io%ation o, any instruction s"eci,ie aboe wi%% resu%t ERO mar/s in your assignment.

9. Answer a%% uestions. O(! #!"&'( +&** $! 4'"!( a )a('% ') !a*#a&'(.

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Assignment Questions BITS