Exam Details
| Subject | statistics | |
| Paper | ||
| Exam / Course | m.sc | |
| Department | ||
| Organization | central university | |
| Position | ||
| Exam Date | 2012 | |
| City, State | telangana, hyderabad |
Question Paper
Entrance Examination M.Sc. Statistics, 2012
Hall Ticket Number I ·1I
Time 2 hours Part A 25 marks
Max. Marks. 100
Part B 75 marks Instructions
1.
Write your Hall Ticket Number on the OMR Answer Sheet given to you. Also write the Hall Ticket Number in the space provided above.
2.
Answers are to be marked on the OMR answer sheet.
3.
Please read the instructions carefully before marking your answers on the OMR answer sheet.
4.
Hand over the question paper along with the OMR answer sheet after the examination.
5.
No additional sheets will be provided. Rough work can be done in the question paper itself/space provided at the end of the booklet.
6.
Calculators are not allowed.
7.
There are a total of 50 questions in Part A and Part B together.
8.
Each question in Part A has only one correct option and there is negative marking.
9.
In Part, B some questions have more than one correct option. All the
correct options have to be marked in the OMR answer sheet otherwise zero marks will be credited
10.
The appropriate answer(s) should be coloured with either a blue or a black ball point or a sketch pen. DO NOT USE A PENCIL.
11.
THE MAXIMUM MARKS FOR THIS EXAMINATION IS 100 AND THERE WILL BE NO INTERVIEW.
Part-A
• Find the correct answer and mark it on the OMR sheet. Each correct answer gets 1 mark and wrong answer gets -0.33 marks..
1. The mean of 15 distinct numbers is 31 and the median is 28, suppose the largest is reduced by 4 and the smallest is increased by 1 and the next one by 3,then which of the statements is correct regarding the mean and median of the modified numbers?
The mean and median remain the same as before.
The mean decreases but the median increases.
1Both the median and mean increase.
the mean increases but the median decreases.
2. Let be the pdf of a continuous random variable defined on JR,
ff is an increasing function on R
f is a continuous function.
f 0 for all x.
f is always bounded.
3. A and B are two independent events with equal probabilities, if P(A UB) 0.75., then
1/4.
3/4.
1/2. 1.
4. Let X be the sample mean,based on a sample Xl, Xn, the maximum likelihood
estimator for (variance) of a normally distributed random variable with mean 1 is
Xl 1. Lti=l (Xi .
n
n
(Xi
n
5. Let X be normally distributed with mean 10 and variance 100, the value of bfor which EIX -bl is least is
O.
10. none of the above.
6. 4 dice have been rolled. What is the probability that the sum is less than 25?
O. 1/2.
1/6. 1.
7. One out of 3 balls in a bag is red and the two are blue, one ball is removed, the probability that one of the remaining two is red is
1/4. 1/3.
2/3.
8. The probability that at least one of A and B occurs is 0.9 and probability that both A and B occur is 0.4, the probability that atmost one of A and B occurs
0.6. 0.5.
0.4. cannot be determined from the given data.
9. How many of 30 balls should be red and how many blue so that the number of possible arrangements is maximized?
Red-lO, Blue-20. Red-O, Blue-30.
Red-25, Blue-5. None of the previous options.
10. The probability density function of a real valued random variable X is -00 x 00. If for some a P(X then
P(X a. P(X I-a.
P(IXI a. P(X a.
11. The sum of 10 real numbers is hundred, the sum of their reciprocals can be
1/3.
3/4. 2.
12. If the rank of 3 x 3 real matrix A is it means that
the determinant of A is zero.
one of the rows of A is a linear combination of other rows.
one of the columns of A is a linear combination of other columns.
the rows of A form a basis in ]R3.
13. The expected value of a random variable X taking positive integer values is further P(X P(X 0.2, P(X 0.3, we can say that
P(X can be equal to 0.16.
P(X is certainly less than 0.16.
P(X can be equal to 0.2.
P(X is more than 0.16.
14. The sum of three numbers is equal to then their product is
at least 4. less than 3.
equal to 3. equal to 4.
15. The correlation coefficient between two random variables X and Y-PX,Y is define
U =2X and V 18 so PU,v is equal to
rA] 1/2.
O. -1/18.
16. Let X and Y be binomial random variables with parameters and respectively, then
P(X P(Y for j ... ,n.
VeX) none of the previous options.
17. Which of the following random variables is bimodal?
1Xl Poisson random variable with parameter 10.
X2 Binomial random variable with parameters
X3 25) normal random variable with mean 10 and variance 25.
X4 exp(5) the exponential random variable with parameter 5.
18. 6 girls GI, G2, .. Ga and 10 boys BI, B2, • .• ,BID are randomly made to sit in a row. What is the probability that none of the girls is at either end?
1/4 3/8 1/2 5/8
19. Given below are marks of 6 students in English and Mathematics
English 62 63· 64 65 66 67
Mathematics 92 92 92 92 92 97
Variances of marks in the two subjects are the same.
Variance of marks in English is less than the variance of marks in Mathematics.
The correlation between the marks in the two subjects is zero.
The correlation between the marks is almost 1.
20. TI and T2 are two unbiased estimators of a parameter however, So
2
to estimate 0 we should use the
mean of the observed values of TI and T2 because we will be using more information then.
observed values of TI and T2 by random selection to be unbiased.
J observed value of TI because it will be certainly closer to 0 than the observed value of T2 .
observed value of TI because it is more likely to be closer to 0 than the observed value of T2•
21. Consider the following linear programming problem.
maximize 4XI 6X2
subject to Xl 2X2 31 2XI X2 25 3XI X2 30 Xl, X2 O.
Which of the following is an optimal solution.
[AJ Xl 6.2, X2 12. Xl 5.8, X2 12.6.
Xl 7.1, X2 12. Xl 10, X2 12.
22. Based on a sample of size n from the population to test Ho /.L . Ito vs HI It> Ito, the most powerful level a test criterion is: reject Ho if X a where X
n n
is the sample mean. Now suppose variance is not 9 but 16, let be the sample size required so that the test criterion is: reject Ho if X a is the most powerful level a test. then
is equal to n. is equal to 2n.
is more than n but less than 2n. is less than n.
00
IOn
23. The series L
n=1 n.
diverges. equal to a positive number greater than 20.
equal to 3. equal to 10.
24. the heights of adult ladies in our country are normally distributed with mean 150cm and variance 49cm2, if P(O Z 0.25 where Z then half the ladies
have heights between
and (150 a)cm.
150cm and (150 2a)cm.
](150-7a)cm and (150 7a)cm.
](150-7a)cm and (150 a)cm.
25. The statement "Ashok and Bharat saw Chandru at the cinema hall" is not true. It means
Chandru was not at the cinema hall.
neither Ashok nor Bharat saw Chandru at the cinema hall.
Bharat was not at the cinema halL
none of the above.
Part-B
•
Questions may have more than one correct option. For the answer to be right all the correct options have to be marked on the OMR sheet. No credit will be given for partially correct answers.
•
Questions may have only one correct option.
•
Find the correct answers and mark them on the OMR sheet. Correct answers (marked in OMR sheet) to a question get 3 marks and zero otherwise.
26. Two events A and B satisfy the following conditions: 0 0 1 and P(AIB) Then
1A and B are mutually exclusive.
1P(BIA)
P(ACIBC) P(AC).
A and B are independent events.
27. Pick up a number from the set ... ,100}. Let A and B denote the events that the selected number is odd and that the selected number is a prime respectively, so
P(AC). P(BIA)
P(BCIAC) P(BC). A and B are independent events.
28. The random variable X is normally distributed with mean 35 and variance 81. So
45. P(X 55) P(X
P(X 45) P(X 15). P(X 45) P(X 25).
29. Bag 1 contains 60 balls, 20 each of them numbered 0,1 and 2. Bag 2 also contains 60 balls. But 25 each are numbered 0 and 1 and 10 are numbered 2. A ball is drawn from each of the bags, let Xl and X2 denote the numbers on the balls drawn from Bag 1
and bag 2 respectively. Then
P(Xl P(X2 0).
P(Xl P(X2 1).
E(Xd E(X2
E E (X21
30. The arithmetic mean and median of 5 distinct natural numbers are both the maximum of the 5 numbers
could be 18.
is at least 19.
is at most 17. is at least 9.
31. 10 numbers are drawn from the set ... IOO} without replacement. The probability that
fA the mean of the selected numbers is more than 5.5 is greater than 0.99.
the median of the selected numbers is 6 is less than 0.0001.
the variance of the selected numbers is more than 8 is 1.
the maximum ofthe selected numbers is more than 90 is greater than 0.5.
32. Consider the function
Ox<0
x n,n ...
f is continuous everywhere.
f is bounded.
f is differentiable everywhere.
f is non-decreasing in x.
33. Xl, X2, X3 are independent and identically distributed random variables with mean and variance 1 Let X 1+X2+Xa and -Xl+2X2+3Xa so
. I
]Yiand Y2 are unbiased estimators for O.
Yi is an unbiased but is not an unbiased estimator for O.
The correlation coefficient PYl,Y2 between YI and is greater than 1/2.
Variance of Yi is less than variance of Y;.
34. Let mm Mn and Vn be the mean, median and variance respectively of the first
natural numbers, remove 1 and n from this set, let and denote the same for the new set, then
35. AI, A2, Aa and are independent events and for then
the probability that at least one of them occurs is 1.
the probability that at least one of them occurs is less than 3/4.
the probability that at most one of them occurs is more than 1/4.
the probability that exactly two of them occur is more than 1/4.
36. X So
P(X 48) P(X 45).
P(X 20) P(X 48).
P(X P(X 54).
P(X 30) P(X 25).
37. X is a random variable with probability mass function P(X pqx-I, X ..., p P q 1. Then
P(X qi.
fB] l.
The next 13 questions have only one correct option.
38. A and B are two events with P(AIB) 3/4. Then P(AIBC)
is equal to 1/3. is equal to 1/2.
is equal to 2/3. cannot be determined from the given data.
39. Let denote a randomly selected point in a square of area 1. What is the probability of the event that IX -YI 1/3
1/3. 2/9.
4/9. 5/9.
40. From a bag containing 6 white balls (all alike), either 1 or 2 or 3 or 4 or 5 or 6 are taken out with probabilities 1/6 each, then the balls drawn are painted red and returned to the bag (now this bag contains at least one red ball). Now a ball is taken from this bag and it is red. What is the probability that the number of balls taken out and painted
red in the beginning was
4/21. 6/21.
1/3. 8/21.
41. A bag contains 100 slips. ni of them numbered n2 are numbered n3 are numbered n4 are numbered 4 and the remaining n5 are numbered 5. 50 draws are made with replacement. The frequency distribution of these 50 numbers is given below:
number 12345 frequency 9 10 11 12 8.
To test the hypothesis that nI, n2, n3, n4 and n5 are equal, the X2 goodness of fit statistic is
O. 1/2. 1/4.
42. The probability distribution of a random variable is as follows X 12 34
where 0 P2 1/2. From the above distribution, PI 2PI P2 P2 we have the following sample of size 6 2. The maximum likelihood
estimate of PI is
1/4. 1/5.
1/6. 1/7.
43. Consider a data set of marks in a public exam. It is found that 75% of them are within 10 from the mean marks. According to Chebychev's inequality the standard deviation of the marks is
less than 4. equal to 5.
equal to 4. more than 5.
44. A coin for which the probability of heads showing up on tossing it is P is tossed 15 times. The first head appeared in the 3rd toss and 6 heads showed up in the 15 tosses, unbiased estimates for P and l/p are respectively
6/15 and 15/6. and 3.
6/15 and 3. 1/3 and 15/6.
45. A coin is tossed 7 times and the outcomes are HTTHHTH, if the probability of the coin showing up heads upon tossing is an unbiased estimate for p2 is
1/2. 2/7.
5/7. 16/49.
46. Let Rl, and R3 be the rows of 3 x 3 non singular real matrix let the first row of B be 2Rl, the second row of B be R2 R3and suppose the third row of B is R2, then
B is singular. rank(B)=3.
rank(A+B)=2. rank(B-A) =2.
47. Let X and Y be independent and identically distributed random variables with probability distributions given by P(X j(j j ... then the value of P(X is in the interval
48. Xl, ... Xn is a random sample from the population. Let X be the sample mean and 8 2 be the statistic an unbiased estimator for p3 is
n-1L...t
i=l
X 3.
]X3-382.
2
3x XX8 .
n·
49. Xl, X2 are a random sample from the variable X with probability mass function P(X X 0,1and p 1 which of the following statements is correct?
1Xl -X2 is not a sufficient statistic for p. •
X is not a sufficient statistic for p.
1(Xl X2 is not an unbiased estimator for p.
]X2 is a sufficient statistic for p.
50. Suppose X is a random variable following exponential distribution with mean 1/A if its median is 0.6 the mean is
1/ log 2. 1/log4.
0.6/ log 2. log 2/0.6.
Hall Ticket Number I ·1I
Time 2 hours Part A 25 marks
Max. Marks. 100
Part B 75 marks Instructions
1.
Write your Hall Ticket Number on the OMR Answer Sheet given to you. Also write the Hall Ticket Number in the space provided above.
2.
Answers are to be marked on the OMR answer sheet.
3.
Please read the instructions carefully before marking your answers on the OMR answer sheet.
4.
Hand over the question paper along with the OMR answer sheet after the examination.
5.
No additional sheets will be provided. Rough work can be done in the question paper itself/space provided at the end of the booklet.
6.
Calculators are not allowed.
7.
There are a total of 50 questions in Part A and Part B together.
8.
Each question in Part A has only one correct option and there is negative marking.
9.
In Part, B some questions have more than one correct option. All the
correct options have to be marked in the OMR answer sheet otherwise zero marks will be credited
10.
The appropriate answer(s) should be coloured with either a blue or a black ball point or a sketch pen. DO NOT USE A PENCIL.
11.
THE MAXIMUM MARKS FOR THIS EXAMINATION IS 100 AND THERE WILL BE NO INTERVIEW.
Part-A
• Find the correct answer and mark it on the OMR sheet. Each correct answer gets 1 mark and wrong answer gets -0.33 marks..
1. The mean of 15 distinct numbers is 31 and the median is 28, suppose the largest is reduced by 4 and the smallest is increased by 1 and the next one by 3,then which of the statements is correct regarding the mean and median of the modified numbers?
The mean and median remain the same as before.
The mean decreases but the median increases.
1Both the median and mean increase.
the mean increases but the median decreases.
2. Let be the pdf of a continuous random variable defined on JR,
ff is an increasing function on R
f is a continuous function.
f 0 for all x.
f is always bounded.
3. A and B are two independent events with equal probabilities, if P(A UB) 0.75., then
1/4.
3/4.
1/2. 1.
4. Let X be the sample mean,based on a sample Xl, Xn, the maximum likelihood
estimator for (variance) of a normally distributed random variable with mean 1 is
Xl 1. Lti=l (Xi .
n
n
(Xi
n
5. Let X be normally distributed with mean 10 and variance 100, the value of bfor which EIX -bl is least is
O.
10. none of the above.
6. 4 dice have been rolled. What is the probability that the sum is less than 25?
O. 1/2.
1/6. 1.
7. One out of 3 balls in a bag is red and the two are blue, one ball is removed, the probability that one of the remaining two is red is
1/4. 1/3.
2/3.
8. The probability that at least one of A and B occurs is 0.9 and probability that both A and B occur is 0.4, the probability that atmost one of A and B occurs
0.6. 0.5.
0.4. cannot be determined from the given data.
9. How many of 30 balls should be red and how many blue so that the number of possible arrangements is maximized?
Red-lO, Blue-20. Red-O, Blue-30.
Red-25, Blue-5. None of the previous options.
10. The probability density function of a real valued random variable X is -00 x 00. If for some a P(X then
P(X a. P(X I-a.
P(IXI a. P(X a.
11. The sum of 10 real numbers is hundred, the sum of their reciprocals can be
1/3.
3/4. 2.
12. If the rank of 3 x 3 real matrix A is it means that
the determinant of A is zero.
one of the rows of A is a linear combination of other rows.
one of the columns of A is a linear combination of other columns.
the rows of A form a basis in ]R3.
13. The expected value of a random variable X taking positive integer values is further P(X P(X 0.2, P(X 0.3, we can say that
P(X can be equal to 0.16.
P(X is certainly less than 0.16.
P(X can be equal to 0.2.
P(X is more than 0.16.
14. The sum of three numbers is equal to then their product is
at least 4. less than 3.
equal to 3. equal to 4.
15. The correlation coefficient between two random variables X and Y-PX,Y is define
U =2X and V 18 so PU,v is equal to
rA] 1/2.
O. -1/18.
16. Let X and Y be binomial random variables with parameters and respectively, then
P(X P(Y for j ... ,n.
VeX) none of the previous options.
17. Which of the following random variables is bimodal?
1Xl Poisson random variable with parameter 10.
X2 Binomial random variable with parameters
X3 25) normal random variable with mean 10 and variance 25.
X4 exp(5) the exponential random variable with parameter 5.
18. 6 girls GI, G2, .. Ga and 10 boys BI, B2, • .• ,BID are randomly made to sit in a row. What is the probability that none of the girls is at either end?
1/4 3/8 1/2 5/8
19. Given below are marks of 6 students in English and Mathematics
English 62 63· 64 65 66 67
Mathematics 92 92 92 92 92 97
Variances of marks in the two subjects are the same.
Variance of marks in English is less than the variance of marks in Mathematics.
The correlation between the marks in the two subjects is zero.
The correlation between the marks is almost 1.
20. TI and T2 are two unbiased estimators of a parameter however, So
2
to estimate 0 we should use the
mean of the observed values of TI and T2 because we will be using more information then.
observed values of TI and T2 by random selection to be unbiased.
J observed value of TI because it will be certainly closer to 0 than the observed value of T2 .
observed value of TI because it is more likely to be closer to 0 than the observed value of T2•
21. Consider the following linear programming problem.
maximize 4XI 6X2
subject to Xl 2X2 31 2XI X2 25 3XI X2 30 Xl, X2 O.
Which of the following is an optimal solution.
[AJ Xl 6.2, X2 12. Xl 5.8, X2 12.6.
Xl 7.1, X2 12. Xl 10, X2 12.
22. Based on a sample of size n from the population to test Ho /.L . Ito vs HI It> Ito, the most powerful level a test criterion is: reject Ho if X a where X
n n
is the sample mean. Now suppose variance is not 9 but 16, let be the sample size required so that the test criterion is: reject Ho if X a is the most powerful level a test. then
is equal to n. is equal to 2n.
is more than n but less than 2n. is less than n.
00
IOn
23. The series L
n=1 n.
diverges. equal to a positive number greater than 20.
equal to 3. equal to 10.
24. the heights of adult ladies in our country are normally distributed with mean 150cm and variance 49cm2, if P(O Z 0.25 where Z then half the ladies
have heights between
and (150 a)cm.
150cm and (150 2a)cm.
](150-7a)cm and (150 7a)cm.
](150-7a)cm and (150 a)cm.
25. The statement "Ashok and Bharat saw Chandru at the cinema hall" is not true. It means
Chandru was not at the cinema hall.
neither Ashok nor Bharat saw Chandru at the cinema hall.
Bharat was not at the cinema halL
none of the above.
Part-B
•
Questions may have more than one correct option. For the answer to be right all the correct options have to be marked on the OMR sheet. No credit will be given for partially correct answers.
•
Questions may have only one correct option.
•
Find the correct answers and mark them on the OMR sheet. Correct answers (marked in OMR sheet) to a question get 3 marks and zero otherwise.
26. Two events A and B satisfy the following conditions: 0 0 1 and P(AIB) Then
1A and B are mutually exclusive.
1P(BIA)
P(ACIBC) P(AC).
A and B are independent events.
27. Pick up a number from the set ... ,100}. Let A and B denote the events that the selected number is odd and that the selected number is a prime respectively, so
P(AC). P(BIA)
P(BCIAC) P(BC). A and B are independent events.
28. The random variable X is normally distributed with mean 35 and variance 81. So
45. P(X 55) P(X
P(X 45) P(X 15). P(X 45) P(X 25).
29. Bag 1 contains 60 balls, 20 each of them numbered 0,1 and 2. Bag 2 also contains 60 balls. But 25 each are numbered 0 and 1 and 10 are numbered 2. A ball is drawn from each of the bags, let Xl and X2 denote the numbers on the balls drawn from Bag 1
and bag 2 respectively. Then
P(Xl P(X2 0).
P(Xl P(X2 1).
E(Xd E(X2
E E (X21
30. The arithmetic mean and median of 5 distinct natural numbers are both the maximum of the 5 numbers
could be 18.
is at least 19.
is at most 17. is at least 9.
31. 10 numbers are drawn from the set ... IOO} without replacement. The probability that
fA the mean of the selected numbers is more than 5.5 is greater than 0.99.
the median of the selected numbers is 6 is less than 0.0001.
the variance of the selected numbers is more than 8 is 1.
the maximum ofthe selected numbers is more than 90 is greater than 0.5.
32. Consider the function
Ox<0
x n,n ...
f is continuous everywhere.
f is bounded.
f is differentiable everywhere.
f is non-decreasing in x.
33. Xl, X2, X3 are independent and identically distributed random variables with mean and variance 1 Let X 1+X2+Xa and -Xl+2X2+3Xa so
. I
]Yiand Y2 are unbiased estimators for O.
Yi is an unbiased but is not an unbiased estimator for O.
The correlation coefficient PYl,Y2 between YI and is greater than 1/2.
Variance of Yi is less than variance of Y;.
34. Let mm Mn and Vn be the mean, median and variance respectively of the first
natural numbers, remove 1 and n from this set, let and denote the same for the new set, then
35. AI, A2, Aa and are independent events and for then
the probability that at least one of them occurs is 1.
the probability that at least one of them occurs is less than 3/4.
the probability that at most one of them occurs is more than 1/4.
the probability that exactly two of them occur is more than 1/4.
36. X So
P(X 48) P(X 45).
P(X 20) P(X 48).
P(X P(X 54).
P(X 30) P(X 25).
37. X is a random variable with probability mass function P(X pqx-I, X ..., p P q 1. Then
P(X qi.
fB] l.
The next 13 questions have only one correct option.
38. A and B are two events with P(AIB) 3/4. Then P(AIBC)
is equal to 1/3. is equal to 1/2.
is equal to 2/3. cannot be determined from the given data.
39. Let denote a randomly selected point in a square of area 1. What is the probability of the event that IX -YI 1/3
1/3. 2/9.
4/9. 5/9.
40. From a bag containing 6 white balls (all alike), either 1 or 2 or 3 or 4 or 5 or 6 are taken out with probabilities 1/6 each, then the balls drawn are painted red and returned to the bag (now this bag contains at least one red ball). Now a ball is taken from this bag and it is red. What is the probability that the number of balls taken out and painted
red in the beginning was
4/21. 6/21.
1/3. 8/21.
41. A bag contains 100 slips. ni of them numbered n2 are numbered n3 are numbered n4 are numbered 4 and the remaining n5 are numbered 5. 50 draws are made with replacement. The frequency distribution of these 50 numbers is given below:
number 12345 frequency 9 10 11 12 8.
To test the hypothesis that nI, n2, n3, n4 and n5 are equal, the X2 goodness of fit statistic is
O. 1/2. 1/4.
42. The probability distribution of a random variable is as follows X 12 34
where 0 P2 1/2. From the above distribution, PI 2PI P2 P2 we have the following sample of size 6 2. The maximum likelihood
estimate of PI is
1/4. 1/5.
1/6. 1/7.
43. Consider a data set of marks in a public exam. It is found that 75% of them are within 10 from the mean marks. According to Chebychev's inequality the standard deviation of the marks is
less than 4. equal to 5.
equal to 4. more than 5.
44. A coin for which the probability of heads showing up on tossing it is P is tossed 15 times. The first head appeared in the 3rd toss and 6 heads showed up in the 15 tosses, unbiased estimates for P and l/p are respectively
6/15 and 15/6. and 3.
6/15 and 3. 1/3 and 15/6.
45. A coin is tossed 7 times and the outcomes are HTTHHTH, if the probability of the coin showing up heads upon tossing is an unbiased estimate for p2 is
1/2. 2/7.
5/7. 16/49.
46. Let Rl, and R3 be the rows of 3 x 3 non singular real matrix let the first row of B be 2Rl, the second row of B be R2 R3and suppose the third row of B is R2, then
B is singular. rank(B)=3.
rank(A+B)=2. rank(B-A) =2.
47. Let X and Y be independent and identically distributed random variables with probability distributions given by P(X j(j j ... then the value of P(X is in the interval
48. Xl, ... Xn is a random sample from the population. Let X be the sample mean and 8 2 be the statistic an unbiased estimator for p3 is
n-1L...t
i=l
X 3.
]X3-382.
2
3x XX8 .
n·
49. Xl, X2 are a random sample from the variable X with probability mass function P(X X 0,1and p 1 which of the following statements is correct?
1Xl -X2 is not a sufficient statistic for p. •
X is not a sufficient statistic for p.
1(Xl X2 is not an unbiased estimator for p.
]X2 is a sufficient statistic for p.
50. Suppose X is a random variable following exponential distribution with mean 1/A if its median is 0.6 the mean is
1/ log 2. 1/log4.
0.6/ log 2. log 2/0.6.