STA301 Final Term Past Paper 2

FINALTERM  EXAMINATION

STA301- Statistics and Probability (Session - 1)

Question No: 1    ( Marks: 1 )    - Please choose one

 10! =………….

       ► 362880

       ► 3628800

       ► 362280

       ► 362800

   

Question No: 2    ( Marks: 1 )    - Please choose one

 When E is an impossible event, then P(E) is:

       ► 2

       ► 0

       ► 0.5

       ► 1

   

Question No: 3    ( Marks: 1 )    - Please choose one

 The value of χ²can never be :

       ► Zero

       ► Less than 1

       ► Greater than 1

       ► Negative

   

Question No: 4    ( Marks: 1 )    - Please choose one

 The curve of the F- distribution depends upon:

       ► Degrees of freedom

       ► Sample size

       ► Mean

       ► Variance

   

Question No: 5    ( Marks: 1 )    - Please choose one

 If X and Y are random variables, then is equal to:

       ►

       ►

       ►

       ►

   

Question No: 6    ( Marks: 1 )    - Please choose one

 In testing hypothesis, we always begin it with assuming that:

       ► Null hypothesis is true

       ► Alternative hypothesis is true

       ► Sample size is large

       ► Population is normal

   

Question No: 7    ( Marks: 1 )    - Please choose one

 For the Poisson distribution P(x) =  the mean value is :

       ►             2

       ► 5

       ►            10                                                      

       ► 0.135

   

Question No: 8    ( Marks: 1 )    - Please choose one

 When two coins are tossed simultaneously, P (one head) is:

       ►

       ►

       ►

       ► 1

   

Question No: 9    ( Marks: 1 )    - Please choose one

 From point estimation, we always get:

       ► Single value

       ► Two values

       ► Range of values

       ► Zero

    

Question No: 10    ( Marks: 1 )    - Please choose one

 The sample variance  is:

       ► Unbiased estimator of

       ► Biased estimator of

       ► Unbiased estimator of

       ► None of these

    

Question No: 11    ( Marks: 1 )    - Please choose one

 Var(4X + 5) =__________

       ► 16 Var (X)

       ► 16 Var (X) + 5

       ► 4 Var (X) + 5

       ► 12 Var (X)

   

Question No: 12    ( Marks: 1 )    - Please choose one

 When f (x, y) is bivariate probability density function of continuous r.v.'s X and Y, then

 is equal to:

       ► 1

       ► 0

       ► -1

       ►

   

Question No: 13    ( Marks: 1 )    - Please choose one

 The area under a normal curve between 0 and -1.75 is

       ► .0401

       ► .5500

       ► .4599

       ► .9599

    

Question No: 14    ( Marks: 1 )    - Please choose one

 When a fair die is rolled, the sample space consists of:

       ► 2 outcomes

       ► 6 outcomes

       ► 36 outcomes

       ►                  16 outcomes

   

Question No: 15    ( Marks: 1 )    - Please choose one

  When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom.

       ► 5

       ► 6

       ► 7

       ► 12

   

Question No: 16    ( Marks: 1 )    - Please choose one

 The F- test statistic in one-way ANOVA is:

       ► SSW / SSE

       ► MSW / MSE

       ► SSE / SSW

       ► MSE / MSW

    

Question No: 17    ( Marks: 1 )    - Please choose one

 The continuity correction factor is used when:

       ► The sample size is at least 5

       ► Both nP and n (1-P) are at least 30

       ► A continuous distribution is used to approximate a discrete distribution

       ► The standard normal distribution is applied

    

Question No: 18    ( Marks: 1 )    - Please choose one

 A uniform distribution is defined by:

       ► Its largest and smallest value

       ► Smallest value

       ► Largest value

       ► Mid value

    

Question No: 19    ( Marks: 1 )    - Please choose one

  Which graph is made by plotting the mid point and frequencies?

       ► Frequency polygon

       ► Ogive

       ► Histogram

       ► Frequency curve

    

Question No: 20    ( Marks: 1 )    - Please choose one

 In a set of 20 values all the values are 10, what is the value of median?

       ► 2

       ► 5

       ► 10

       ► 20

   

Question No: 21    ( Marks: 1 )

 If  =,=,= and =

Then find F (1)

   

Question No: 22    ( Marks: 2 )

 Write down the formula of mathematical expectation.

e=(w * p) + (-v *1). e

   

Question No: 23    ( Marks: 3 )

 Discuss the statistical independence of two discrete random variables:

Question No: 24    ( Marks: 3 )

 For given data calculate the mean and standard deviation of sampling distribution of mean if the sampling is down without replacement.

   

Question No: 25    ( Marks: 3 )

 Elaborate the Least Significant Difference (LSD) Test.

 

Question No: 26    ( Marks: 3 )

 State the Bayes’ Theorem.

Question No: 27    ( Marks: 5 )

 The means and variances of the weekly incomes in rupees of two samples of workers are given in the following table, the samples being randomly drawn from two different factories:

Calculate the 90% confidence interval for the real difference in the incomes of the workers from the two factories.

   

Question No: 28    ( Marks: 5 )

 From the given data and .

Carry out the significance test for the stated hypothesis.

   

Question No: 29    ( Marks: 5 )

 Given the Probability density function

.

Compute the distribution function F(x).

   

Question No: 30    ( Marks: 10 )

 

a)         Verify that f(x,y) is a joint

            density function.

b)         Calculate   

   

Question No: 31    ( Marks: 10 )

 Let be a random sample of size 3 from a population with mean   

Consider the following two estimators of the mean

Which estimator should be preferred?