University Of Pune Question Paper FYMCA (Engg. Faculty)
PROBABILITY AND STATISTICS
(Semester - I) (2008 Pattern) (510904)
MAY 2013 EXAMINATIONS
Time: 3 Hours] [Max. Marks : 70
Instructions to the candidates:
1) Answers to the two sections should be written in separate answer books.
2) Neat diagrams must be drawn wherever necessary.
3) Figures to the right side indicate full marks.
4) Q1 OR Q2, Q3 OR Q4, Q5 OR Q6, Q7 OR Q8, Q9 OR Q10, Q11 OR Q12
5) Use of probability table, electronic pocket calculator is allowed.
6) Assume Suitable data if necessary.
SECTION I
Q1) a) Two marbles are drawn in succession from a box containing 25 blue, 20 yellow,
15 orange and 35 red marbles, with replacement being made after each drawing.
Find the probability that i) both are red ii) first is yellow and second is blue
iii) first is red and second is orange.
[6]
b) A company produces items using three different machines A, B and C.
Production of these machines is 25%, 30% and 45% respectively of the total
production. It is found from experience that 4%, 5% and 6% of machines A, B
and C respectively are defective. On general inspection of entire production one
item is selected at random and found to be defective. Find the probability that it is
produced by machine B.
[6]
OR
Q2) a) A certain firm has plants A, B and C producing 35%, 15% and 50% respectively
of the total output. The probabilities of non-defective product from these plants
are 0.75, 0.95 and 0.85 respectively. An item is selected from the total output of
these plants and found to be defective. What is the probability that it is produced
by plant C?
[6]
b) State and prove Baye’s theorem. [6]
Q3) a) Define with example:
i) Probability density function
ii) Event
iii) Marginal Probability
[6]
b) If the probability that an individual suffers a bad reaction due to injection is
0.001. Determine the probability that exactly 3 out of 2000 individuals suffer a
bad reaction. (Use Poisson distribution)
[6]
OR
[4366]-104 Page 2 of 3
Q4) a) A continuous random variable has probability density function
K(y+1), 2<y<4
f(y) =
o otherwise
Find i) k ii) p(y<3.2) iii) p(2.9<y<3.2)
[6]
b) Explain the terms:
i) Independent events
ii) Axioms of Probability
iii) Conditional probability.
[6]
Q5) a) Obtain mean and variance of Uniform distribution. [6]
b) Let (X, Y) be a discrete bivariate random variable with the following p.m.f.
Y
X
1 2 3
1 1/12 1/6 0
2
0 1/9 1/15
3
1/18 1/4 2/15
Find marginal and conditional probability mass distribution for X and Y.
[5]
OR
Q6) a) Determine the constant b such that a joint p.d.f. of bivariate random variables X
and Y is given by :
3xy for 0<x<1, 0<y<b
f(x,y) =
0 otherwise
[6]
b) Explain the following probability distributions with suitable examples
i) Poisson Distribution
ii) Normal Distribution
[5]
SECTION II
Q7) a) What is point estimator and point estimate? What properties of estimator make
it a good estimator?
[6]
b) Find the mean and variance of sampling distribution of mean for the population
4, 8, 7, 6, 2, 9 by drawing a sample of size 2 with replacement and without
replacement.
[6]
OR
[4366]-104 Page 3 of 3
Q8) a) Explain the following terms:
i) Confidence Interval
ii) Estimation
iii) Central limit Theorem
[6]
b) Explain significance testing? How does it differ from hypothesis testing? [6]
Q9) a) The length of life of certain battery is approximately normally distributed with
mean 300 days and standard deviation 50 days. If a random sample of 25
batteries has a life of 275 days. Test the null hypothesis that µ = 300 days
against the alternate hypothesis µ ≠ 300 days at 5 % level of significance.
[6]
b) Explain the following terms:
i) Null hypothesis and research hypothesis.
ii) Type I and type II errors.
iii) Critical region for the test
[6]
OR
Q10) a) Write a short note on student’s t-distribution. [6]
b) The following data give the number of aircraft accidents that occurred during
the various days of a week.
Day : Mon Tue Wed Thu Fri Sat
Number of accidents: 15 19 13 12 16 15
Test whether the accidents are uniformly distributed over the week. (Use x
2
Test)
[6]
Q11) a) Explain Statistical Quality Control (SQC) with its advantages and limitations. [5]
b) Given below are the values of sample mean X and sample range R for 10 samples
each of size 5. Draw the appropriate mean and range charts & comment on the
state of control of the process.
Sample no : 1 2 3 4 5 6 7 8 9 10
Mean : 11.0 10.9 11.5 11.1 11.7 11.0 11.0 12.0 12.4 11.4
Range : 2.4 1.4 1.7 0.7 0.8 0.7 1.1 2.0 2.1 1.4
[6]
OR
Q12) a) Explain the x
2
test as a test of goodness of fit. Write the steps. [5]
b) Write note on range chart.
PROBABILITY AND STATISTICS
(Semester - I) (2008 Pattern) (510904)
MAY 2013 EXAMINATIONS
Time: 3 Hours] [Max. Marks : 70
Instructions to the candidates:
1) Answers to the two sections should be written in separate answer books.
2) Neat diagrams must be drawn wherever necessary.
3) Figures to the right side indicate full marks.
4) Q1 OR Q2, Q3 OR Q4, Q5 OR Q6, Q7 OR Q8, Q9 OR Q10, Q11 OR Q12
5) Use of probability table, electronic pocket calculator is allowed.
6) Assume Suitable data if necessary.
Q1) a) Two marbles are drawn in succession from a box containing 25 blue, 20 yellow,
15 orange and 35 red marbles, with replacement being made after each drawing.
Find the probability that i) both are red ii) first is yellow and second is blue
iii) first is red and second is orange.
[6]
b) A company produces items using three different machines A, B and C.
Production of these machines is 25%, 30% and 45% respectively of the total
production. It is found from experience that 4%, 5% and 6% of machines A, B
and C respectively are defective. On general inspection of entire production one
item is selected at random and found to be defective. Find the probability that it is
produced by machine B.
[6]
OR
Q2) a) A certain firm has plants A, B and C producing 35%, 15% and 50% respectively
of the total output. The probabilities of non-defective product from these plants
are 0.75, 0.95 and 0.85 respectively. An item is selected from the total output of
these plants and found to be defective. What is the probability that it is produced
by plant C?
[6]
b) State and prove Baye’s theorem. [6]
Q3) a) Define with example:
i) Probability density function
ii) Event
iii) Marginal Probability
[6]
b) If the probability that an individual suffers a bad reaction due to injection is
0.001. Determine the probability that exactly 3 out of 2000 individuals suffer a
bad reaction. (Use Poisson distribution)
[6]
OR
[4366]-104 Page 2 of 3
Q4) a) A continuous random variable has probability density function
K(y+1), 2<y<4
f(y) =
o otherwise
Find i) k ii) p(y<3.2) iii) p(2.9<y<3.2)
[6]
b) Explain the terms:
i) Independent events
ii) Axioms of Probability
iii) Conditional probability.
[6]
Q5) a) Obtain mean and variance of Uniform distribution. [6]
b) Let (X, Y) be a discrete bivariate random variable with the following p.m.f.
Y
X
1 2 3
1 1/12 1/6 0
2
0 1/9 1/15
3
1/18 1/4 2/15
Find marginal and conditional probability mass distribution for X and Y.
[5]
OR
Q6) a) Determine the constant b such that a joint p.d.f. of bivariate random variables X
and Y is given by :
3xy for 0<x<1, 0<y<b
f(x,y) =
0 otherwise
[6]
b) Explain the following probability distributions with suitable examples
i) Poisson Distribution
ii) Normal Distribution
[5]
SECTION II
Q7) a) What is point estimator and point estimate? What properties of estimator make
it a good estimator?
[6]
b) Find the mean and variance of sampling distribution of mean for the population
4, 8, 7, 6, 2, 9 by drawing a sample of size 2 with replacement and without
replacement.
[6]
OR
[4366]-104 Page 3 of 3
Q8) a) Explain the following terms:
i) Confidence Interval
ii) Estimation
iii) Central limit Theorem
[6]
b) Explain significance testing? How does it differ from hypothesis testing? [6]
Q9) a) The length of life of certain battery is approximately normally distributed with
mean 300 days and standard deviation 50 days. If a random sample of 25
batteries has a life of 275 days. Test the null hypothesis that µ = 300 days
against the alternate hypothesis µ ≠ 300 days at 5 % level of significance.
[6]
b) Explain the following terms:
i) Null hypothesis and research hypothesis.
ii) Type I and type II errors.
iii) Critical region for the test
[6]
OR
Q10) a) Write a short note on student’s t-distribution. [6]
b) The following data give the number of aircraft accidents that occurred during
the various days of a week.
Day : Mon Tue Wed Thu Fri Sat
Number of accidents: 15 19 13 12 16 15
Test whether the accidents are uniformly distributed over the week. (Use x
2
Test)
[6]
Q11) a) Explain Statistical Quality Control (SQC) with its advantages and limitations. [5]
b) Given below are the values of sample mean X and sample range R for 10 samples
each of size 5. Draw the appropriate mean and range charts & comment on the
state of control of the process.
Sample no : 1 2 3 4 5 6 7 8 9 10
Mean : 11.0 10.9 11.5 11.1 11.7 11.0 11.0 12.0 12.4 11.4
Range : 2.4 1.4 1.7 0.7 0.8 0.7 1.1 2.0 2.1 1.4
[6]
OR
Q12) a) Explain the x
2
test as a test of goodness of fit. Write the steps. [5]
b) Write note on range chart.
0 comments:
Pen down your valuable important comments below