TYBA- SemesterVI-Statistics- Sample Questions

Statistics Paper IV -Proabability and Sampling Distribution-

Paper Code - 86529

1. If X and Y are independent random variables with moment generating functions Mx

(t) and My (t) then moment generating function of X+Y is Mx+y (t) =

(A)Mxy (t) (B) Mx (t) My (t) (C)M(XYt) (D)M(X+Y)t

2. Coefficient of kurtosis is measured as

(A)

(B) )

(C )

- 3 (D)

3. Let (X,Y) be a bivariate random variable with joint p.d.f f(x,y) . if g 2 (y/x) is a conditional

p.d.f of Y given x , the conditional expectation of Y given x is denoted by ……

(A ) E(y/x) = x g2 ( y/x) (B) E(y/x) =

g2 (y/x) dy (C) E(y/x)

=

(D) E(X) =

4. For a random variable X follows Uniform(3,9) distribution then its mean is …..

(A)1 (B) 6 (D) 0

5. For a random variable X following exponential distribution the value of

P[X ≥ 8 / X ≥ 3] is equal to …..

(A) P[X ≥ 5] (B) P[X<5] (C) P[ X=5] (D) P[x>3]

6. A continuous random variable X follows Beta distribution of second type , then the value of

………..

(A) 0.5 (B) 0.8 (C) 1 (D) -0.5

7. For a random variable X following N( ) the value of fourth central moment 4 is……

(A) 0 (B) (C) (D)

8. In a sample of 10 observations , the sum of squared deviation of items from the mean was

49.5 . In another sample of 8 observations , the value was found to be 28.4 the test

statistics to test the difference in variations is …………

(A) t -test (B) chi-square test (C)F-test (D) normal

9. If a random variable follows t – distribution with 5 degrees of freedom then mean is…..

(A) 5 (B) 0 ( C) 2 ( D) 3

10. Suppose X1 , X2 , X3 , ……… X15 be a random sample from a normal population with

known mean .Then to test H0 : the

appropriate test statistic is ………..

(A)

(B)

(c)

( D)

Statistics Paper V - Analysis of Variance, Designs of Experiments and R software

Paper Code - 86562

1. Which of the following is not required assumption for analysis of variance?

a. The random variable of interest for each population has a normal probability distribution

b. The variance associate with random variable must be same for each population

c. At least two population are under consideration

d. Population have equal means

2. Analysis of variance is a statistical method of comparing the ________ of several populations

a. standard deviations

b. Variances

c. Means

d. Proportions

3. Which of the following is not a part of Replication?

a. The repetition of the treatments under investigation

b. Replication serves to reduce experimental error

c. Its helps to obtain more precise estimates of the treatment effects

d. Process of assigning the treatments to various experimental units

4. Which of the following is not principle of design of experiment?

a. Replication

b. Experimental error

c. Local control

d. Randomization

5. A design in which the treatments are assigned to the experimental unit completely at random.

a. ANOCOVA.

b. RBD

c. CRD

d. LSD

6. The simplest type of the basic designs.

a. CRD.

b. RBD.

c. ANOCOVA.

d. LSD

7. In case of RBD, Blocks should be made orthogonal of

a. Variation

b. Treatment

c. Standard error.

d. Experimental units

8. In case of RBD, each treatment will occur only once in each

a. Experiment.

b. Line

c. Block.

d. Sample

9. If there are two sources of variations, we introduce

a. RBD.

b. CRD

c. Latin square design

d. Split plot design.

10. Here we make two blocks. The row wise variation is controlled by making column wise block

and similarly the column wise variation is controlled by row wise blocking.

a. RBD.

b. CRD

c. Latin square design.

d. Split plot design

Statistics Paper VI – Applied Statistics – II

Paper Code - 86599

1. As simulation is not an analytical model, therefore, result of simulation must be viewed as-

a. unrealistic

b. exact

c. approximation

d. simplified

2. If x0 = 45, a = 15 and m=100, using congruential method, the first pseudorandom number generated is –

a. 0.40

b. 0.75

c. 0.19

d. 0.56

3. The number of units expected to be sold is uniformly distributed between 100 and 450. If r is a

random number between 0 and 1, then the proper expression for sales is-

a. 100. R

b. r + 450

c. 100 + 450 r

d. 100 + r (350)

4. Studying the dependence of a variable on only a single explanatory variable is known as-

a. One-variable regression analysis

b. Two-variable regression analysis

c. Three variable regression analysis

d. Multiple regression analysis

5. Data collected at a point in time is called-

a. Cross-sectional data

b. Time series data

c. Pooled data

d. Panel data

6. = + + represents-

a. Sample regression function

b. Population regression function

c. Nonlinear regression function

d. Estimate of regression function

7. A regression model in which more than one independent variable is used to predict the

dependent variable is called-

a. a simple linear regression model

b. a multiple regression model

c. an independent model

d. none of the above

8. Heteroscedasticity means that –

a. All X variables cannot be assumed to be homogeneous

b. The variance of the error term is not constant

c. The observed units have no relation

d. The X and Y are not correlated

9. In a regression model = , F – test is seen to be statistically

significant at less than 5 percent level of significance but the coefficients and are seen to

be statistically insignificant. This means that-

a. Two coefficients are highly correlated

b. Two variables are highly correlated

c. Two variables are perfectly correlated

d. Two variables are not correlated

10. Suppose that R-square value of a bivariate regression of Y on X is 0.64.

Which of the following is necessarily true?

a. The correlation coefficient between X and Y is 0.8

b. The correlation coefficient is –0.8

c. The correlation coefficient is 0

d. The correlation coefficient is either 0.8 or –0.8