APRIL 2023 51276/SP3AB

Time : Three hours Maximum : 75 marks

PART A — (10  2 = 20 marks)

Answer any TEN questions, each in 30 words.

1. Define sample.
©õv› Áøμ¯Ö.

2. What are types of events in statistics?

¦ÒÎÂÁμ[PÎÀ {PÌÄPÎß ÁøPPÒ ¯õøÁ?

3. Define distribution.
Â{÷¯õP® Áøμ¯Ö.

4. What are the functions distributions?

{PÌÄPÎß £oPÒ ¯õøÁ?

5. What is the importance of continuous distribution?

öuõhº {PÌÄPÎß •UQ¯zxÁ® GßÚ?

6. How is a normal distribution related to probability

distribution?
\õuõμn Â{÷¯õP® GÆÁõÖ {PÌuPÄ
Â{÷¯õPzxhß öuõhº¦øh¯x?
7. What is standardized normal distribution?
u쨣kzu¨£mh \õuõμn Â{÷¯õP® GßÓõÀ
GßÚ?
8. How is standard normal calculated?
{ø»¯õÚ \õuõμn {ø» GÆÁõÖ ¦Òΰ¯¼À
PnUQh¨£kQÓx?
9. What are the six steps of hypothesis testing?
AÝ©õÚ ÷\õuøÚPÎß BÖ •UQ¯ {ø»PÒ
¯õøÁ?
10. Which test can be used to compare the two means?
G¢u ÷\õuøÚ°ÚõÀ Cμsk \μõ\›PÒ
J¨¤h¨£kQÓx?
11. What data is not normally distributed?
G¢u uPÁÀPÒ ö£õxÁõP Â{÷¯õQUP¨£hÂÀø»?
12. Why do we use standard normal distribution?
u쨣kzu¨£mh \õuõμn Â{÷¯õP® Hß
£¯ß£kzu ÷Ásk®?
PART B — (5  5 = 25 marks)
Answer any FIVE questions, each in 200 words.
13. Describe about Binomial distribution.
ø£Úõª¯À £μÁÀ £ØÔ ÂÍUSP.
14. Mention about cumulative distribution.
Jmkö©õzu Â{÷¯õP •øÓ £ØÔ GÊxP.

2 51276/SP3AB
15. What are the properties of normal distribution?

\õuõμn Â{÷¯õP •øÓ°ß £¯ß£õkPÒ ¯õøÁ?

16. Comment on density function.

Ahºzv ö\¯À£õkPÒ £ØÔ GÊxP.

17. Write notes on students t- distribution.

©õnÁºPÎß i Â{÷¯õP •øÓ £ØÔ GÊxP.

18. What are the limitations of probability?

{PÌuPÄ Á쮦PÒ ¯õøÁ?

19. Comment on independent events.

_¯õwÚ {PÌÄPÒ £ØÔ GÊxP.

PART C — (3  10 = 30 marks)

Answer any THREE questions, each in 500 words.

20. Give an account on Axiomatic approach of

probability.

BUê÷¯õ©iU {PÌuPÄ AqS•øÓ £ØÔ

›ÁõP GÊxP.

21. Write an essay on Poisson distribution in

statistics.

¦Òί¼À £õ´\õß £μÁÀ £ØÔ Pmkøμ GÊxP.

3 51276/SP3AB
22. The length of human pregnancies from conception
to birth approximates a normal distribution with a
mean of 267 days and a standard deviation of
16 days. What proportion of all pregnancies will
last between 240 and 270 days (roughly between 8
and 9 months)? Find out the normal distribution.
©Ûu CÚzvß P¸ÄØÓ |õÒ •uÀ, SÇ¢øu ¤Ó¨¦
Áøμ \μõ\›¯õP \õuõμn {PÌÄhß \μõ\› |õmPÒ
267 ©ØÖ® {ø»¯õÚ Â»PÀ Gߣx 16 |õmPÒ
•ß ©ØÖ® ¤ß C¸US®. P¸ÄØÓ uõ´©õºPÎß
¤Ó¨¦ ÂQu® Gߣx 240 |õmPÒ •uÀ
270 |õmPÒ Áøμ (\μõ\›¯õP 8 •uÀ 9 ©õu®
Áøμ). CvÀ \õuõμn {PÌuPÄ GßÚ Gߣøu
Psk¤i.

23. Find the t-test value for the following two sets of
values: 7, 2, 9, 8 and 1,2,3,4.
i ÷\õuøÚø¯ Akzx Á¸® Cμsk ÷\õuøÚ
©v¨¦PÐhß Eu²hß Psk¤iUP 7, 2, 9, 8
©ØÖ® 1, 2, 3, 4.

24. Discuss on types and applications of ANOVA test.

A÷ÚõÁõÂß ÁøPPÒ ©ØÖ® Auß £¯ß£õkPÒ
£ØÔ ÂÁ›.

——————–––––—

4 51276/SP3AB
NOVEMBER 2023 51276/SP3AB

Time : Three hours Maximum : 75 marks

PART A — (10 × 2 = 20 marks)

Answer any TEN questions, each in 30 words.

1. Define random variable.
\©Áõ´¨¦ ©õÔ Áøμ¯Ö.
2. State addition theorem of probability.
{PÌuPÂß TmhÀ ÷uØÓzøu TÖ.
3. Find the mean of Poisson distribution.
£õ´\õß £μÁ¼ß \μõ\›ø¯U PõsP.
4. Find m.g.f. of binomial distribution.
D¸Ö¨¦ £μÁ¼ß m.g.f. I PõsP.
5. Define exponential distribution.
Av÷ÁP £μÁø» Áøμ¯Ö.
6. Find mean of normal distribution.
C¯À{ø» £μÁ¼ß \μõ\›ø¯U PõsP.
7. Write area property of normal distribution.
C¯À{ø» £μÁ¼ß £μ¨¦ £sø£ GÊxP.
8. What are the two types of error?
Cμsk ÁøP¯õÚ ¤øÇPÒ ¯õøÁ?
9. What are the types of sampling?
©õv› Gkzu¼ß ÁøPPÒ ¯õøÁ?
10. Define students t-distribution.
©õnÁºPÒ i&£μÁø» Áøμ¯Ö.
11. Define Chi-Square distribution.
øP--&ÁºUP £μÁø» Áøμ¯Ö.
12. Define null hypothesis.
§ä¯ P¸x÷PõÒ Áøμ¯Ö.

PART B — (5 × 5 = 25 marks)

Answer any FIVE questions, each in 200 words.

13. State and prove multiplication theorem of

probability.
{PÌuPÂß ö£¸UPÀ ÷uØÓzøuU TÔ {¹¤.
14. State and prove Baye’s theorem.
÷£°ß ÷uØÓzøuU TÔ {¹¤UPÄ®.
15. Let X be a random variable with the following
probability distribution :
x: 1 2 3
P(X = x) : 0.7 0.2 0.1
Find E(X) and E X 2 ( ) and using the laws of
expectation, evaluate E (4 X + 2) .
2

2 51276/SP3AB
 ¤ßÁ¸® {PÌuPÄ £μÁ¾hß X J¸ ^μØÓ ©õÔ¯õP
C¸UPmk® :
x: 1 2 3
P(X = x) : 0.7 0.2 0.1

E(X) ©ØÖ® ( )
E X2 BQ¯ÁØøÓU PshÔ¢x,
Gvº£õº¨¦ ÂvPøͨ £¯ß£kzv, E (4 X + 2)2 I
©v¨¤kP.

16. Obtain the mean and variance of normal

distribution.
C¯À{ø» £μÁ¼ß \μõ\› ©ØÖ® ©õÖ£õmøh¨
ö£ÓÄ®.

17. A normal population has a mean of 0.1 and

standard deviation of 2.1. Find the probability that
mean of sample of size 900 will be negative.
J¸ C¯À£õÚ ©UPÒöuõøP°À \μõ\› 0.1 ©ØÖ®
{¯©a\õ´Ä 2.1 GÛÀ, 900 AÍÄ ©õv›°ß
Gvº©øÓ¯õP C¸US® {PÌuPÄ PshԯĮ.

18. Discuss about purposive sampling.

vmhªmh ©õv› £ØÔ ÂÁõvUP.

19. Explain the large sample test with respect to

standard deviation.
{¯©a\õ´Ä SÔzx ö£›¯ ©õv› ÷\õuøÚø¯
ÂÍUSP.
3 51276/SP3AB
 PART C — (3 × 10 = 30 marks)
Answer any THREE questions, each in 500 words.
20. The contents of urns I, II and III are as follows :
4 White, 3 Black and 2 Red.
5 White, 2 Black and 3 Red, and
6 White, 1 Black and 2 Red, One urn is chosen at
random and two balls drawn. They happen to be
white and red. What is the probability that they
come from urns I, II or III?
I, II ©ØÖ® III P»\[PÎß EÒÍhUP[PÒ
¤ßÁ¸©õÖ :
4 öÁÒøÍ, 3 P¸¨¦ ©ØÖ® 2 ]Á¨¦,
5 öÁÒøÍ, 2 P¸¨¦ ©ØÖ® 3 ]Á¨¦, ©ØÖ®
6 öÁÒøÍ, 1 P¸¨¦ ©ØÖ® 2 ]Á¨¦, J¸ P»\®
^μØÓ •øÓ°À ÷uº¢öukUP¨£mk Cμsk £¢xPÒ
Áøμ¯¨£mhx. AøÁ öÁÒøÍ ©ØÖ® ]Á¨¦
{ÓzvÀ C¸US®. AøÁ I, II AÀ»x III
P»\[PÎÀ C¸¢x Á¸ÁuØPõÚ {PÌuPÄ GßÚ?
21. Find the first four non central moments of Poisson
Distribution.
£õ´\õß £μÁ¼ß •uÀ |õßS ø©¯©ØÓ
u¸n[PøÍU PshԯĮ.
22. Write down the properties of exponential
distribution.
Av÷ÁP £μÁ¼ß £s¦PøÍ GÊuÄ®.
23. Discuss the ANOVA test.
ANOVA ÷\õuøÚ £ØÔ ÂÁõv.
24. Explain the single mean test based on normal
distribution.
C¯À{ø» £μÁ¼ß Ai¨£øh°À J¸ \μõ\›
÷\õuøÚø¯ ÂÍUSP.
——————–––––—
4 51276/SP3AB
NOVEMBER 2022 51276/SP3AB

Time : Three hours Maximum : 75 marks

PART A — (10 × 2 = 20 marks)

Answer any TEN questions each in 30 words.

1. What is probability
{PÌuPÄ GßÓõÀ GßÚ?

2. Independent events
_¯õwÚ {PÌÄPÒ.

3. Define theory in statistics.

¦ÒÎÂÁμ ÷Põm£õk £ØÔ Áøμ¯Ö.

4. Bernoulli.
ö£º÷Úõ¼

5. What are the 4 properties of a normal

distribution?
\õuõμn Â{÷¯õPzvß |õßS £s¦PÒ ¯õøÁ?

6. What is an example of a continuous probability

distribution?
öuõhºa]¯õÚ {PÌuPÄ Â{÷¯õP® £ØÔ
GkzxUPõmk GÊxP.

7. What are the types of discrete distributions?

uÛzxÁ©õÚ Â{÷¯õP ÁøPPÒ ¯õøÁ?
8. What are four common types of continuous
distribution?
öuõhºa]¯õÚ Â{÷¯õPzvß |õßS ö£õxÁõÚ
ÁøPPÒ ¯õøÁ?

9. What is hypothesis testing used for?

AÝ©õÚ ÷\õuøÚ GuØS £¯ß£kQÓx?

10. How do you do a two sample t-test?

Cμsk ©õv› i&÷\õuøÚ •øÓø¯ GÆÁõÖ
ö\´Áõ´?

11. Why is normal distribution important?

\õuõμn Â{÷¯õPzvß •UQ¯zxÁ® GßÚ?

12. What are the three main properties of

distribution?
Â{÷¯õPzvß ‰ßÖ •UQ¯ £s¦PÒ ¯õøÁ?

PART B — (5 × 5 = 25 marks)

Answer any FIVE questions each in 200 words.

13. Write notes on random experiments?

^μØÓ ÷\õuøÚPÒ £ØÔ GÊxP.

14. Comment on binomial distribution.

C¸ÁøP Â{÷¯õP •øÓ £ØÔ SÔ¨¦ GÊxP.

15. List out the functions of cumulative distribution.

Jmkö©õzu Â{÷¯õP •øÓ°ß £¯ß£õkPøÍ
Á›ø\¨£kzxP.
2 51276/SP3AB
16. Describe about sampling distributions.
©õv› Â{÷¯õP •øÓ £ØÔ ÂÍUSP.
17. Write notes on testing of hypothesis.
P¸x÷PõÎß ÷\õuøÚ £ØÔ GÊxP.
18. Explain the properties of density.
Ahºzv°ß £s¦PøÍ ÂÍUSP.
19. Describe about Bayes Theorem.
÷£¯ì ÷uØÓ® £ØÔ ÂÍUSP.
PART C — (3 × 10 = 30 marks)
Answer any THREE questions each in 500 words.

20. Discuss on probability and its limitations.

{PÌuPÄ ©ØÖ® Auß Á쮦PÒ £ØÔ Â›ÁõP
ÂÁ›.
21. Write an essay on discrete probability mass
function.
uÛzxÁ©õÚ {PÌuPÄ ©ØÖ® AvP ö\¯À£õk
£ØÔ Pmkøμ GÊxP.
22. The average number of acres burned by forest and
range fires in a large New Mexico county is 4,300
acres per year, with a standard deviation of 750
acres. The distribution of the number of acres
burned is normal. What is the probability that
between 2,500 and 4,200 acres will be burned in
any given year?

3 51276/SP3AB
 ö£›¯ |õhõÚ ö©U]÷PõÂÀ PõkPÎÀ £μÁUTi¯
w £zvÚõÀ Qmhzumh 4,300 HUPº {»[PÒ
Á¸h¢÷uõÖ® w°À P¸SQßÓÚ. CvÀ 750 HUPº
PõkPÒ {ø»¯õÚ Â»PÀ Ehß Põn¨£kQÓx.
CvÀ Â{÷¯õP •øÓ Gߣx GÆÁÍÄ HUPº
PõkPÒ w°À P¸Q EÒÍÚ GߣuõS®. 2500 US®
©ØÖ® 4,500 HUPº Á¸h¢÷uõÖ® G›¢u PõkPÎß
{PÌuPÄ GßÚ Gߣøu Psk¤iUP.

23. Write an essay on chi-square distribution and its

importance.
]&\xμ Â{÷¯õP® ©ØÖ® Auß •UQ¯zxÁ® £ØÔ
Pmkøμ GÊxP.

24. Newborn babies are more likely to be boys than

girls. A random sample found 13,173 boys were
born among 25,468 newborn children. The sample
proportion of boys was 0.5172. Is this sample
evidence that the birth of boys is more common
than the birth of girls in the entire population?
¦vuõP¨ ¤ÓUPUTi¯ SÇ¢øuPÎÀ ö£s
SÇ¢øuPøÍ Âh Bs SÇ¢øuPøÍ
¸®¦QßÓÚº. ö©õzu® ¤Ó¢u 25,468
SÇ¢øuPÎÀ 13,173 Bs SÇ¢øuPÒ
¤Ó¢xÒÍÚº Gߣx ^μØÓ ©õv›. A¨£i¨ ¤Ó¢u
Bs SÇ¢øuPÎß ©õv› ÂQu® Gߣx 0.5172
BP C¸¢ux. uØö£õÊx ö©õzu® ¤Ó¢u
SÇ¢øuPÎß GsoUøP°À AvP£m\©õP Bs
SÇ¢øuPÒ C¸¢ux Gߣøu ÷\õuøÚ ÂQuzvß
Ai¨£øh°À Psk¤iUP.

——————–––––—

4 51276/SP3AB