Section A: Probability & Distributions
1. The probability of an impossible event is:
A) 0 B) 1 C) 0.5 D) ∞
✅ Answer: A
📘 Explanation: An impossible event cannot occur, so its probability = 0.
2. The sum of probabilities of all exhaustive events equals:
A) 0 B) 1 C) 100 D) Depends on events
✅ Answer: B
📘 Because all possible outcomes together make probability 1.
3. If A and B are independent, =
A) B) C) D) 0
✅ Answer: C
📘 For independent events, joint probability is product of individual probabilities.
4. The expected value of a constant is:
A) 0 B) The constant itself C) 1 D) Undefined
✅ Answer: B
📘 Expected value (mean) of a constant is the constant itself.
5. In a normal distribution, the mean, median, and mode are:
A) Different B) Equal C) Opposite D) Undefined
✅ Answer: B
📘 The normal curve is symmetric, so all three are equal.
6. The Poisson distribution is used for:
A) Continuous data B) Rare discrete events C) Large samples D) Normal data
✅ Answer: B
📘 Poisson models rare events (like accidents per hour).
7. The sum of probabilities in a binomial distribution equals:
A) 0 B) n C) 1 D) Mean
✅ Answer: C
📘 The total of all probabilities always sums to 1.
8. In a normal distribution, about 95% observations lie within:
A) ±1σ B) ±2σ C) ±3σ D) ±4σ
✅ Answer: B
📘 According to the empirical rule, 95% of data lies within 2 standard deviations.
9. If mean = 50 and variance = 25, then standard deviation =
A) 5 B) 25 C) 2 D) 10
✅ Answer: A
📘
10. Central Limit Theorem implies that:
A) Population distribution becomes normal
B) Sample mean becomes normal for large n
C) Sample variance = population variance
D) Mean = 0
✅ Answer: B
📘 CLT → sampling distribution of mean → normal as n increases.
Section B: Descriptive Statistics
11. Mean of 5, 10, 15 is:
A) 10 B) 15 C) 12 D) 30
✅ Answer: A
📘
12. Median of {1, 3, 3, 6, 7, 8, 9} =
A) 3 B) 6 C) 7 D) 5
✅ Answer: B
📘 Middle term = 6.
13. The most frequent value in a dataset is called:
A) Mean B) Median C) Mode D) Range
✅ Answer: C
📘 Mode = most occurring value.
14. Range =
A) Mean – median B) Max – Min C) SD² D) Mode + mean
✅ Answer: B
📘 Range measures total spread of data.
15. The coefficient of variation (CV) =
A) B) C) D)
✅ Answer: B
📘 CV measures relative dispersion.
16. If r = +1, then correlation is:
A) Perfect positive B) Perfect negative C) No correlation D) Moderate
✅ Answer: A
📘 +1 → perfect positive linear relationship.
17. Karl Pearson’s r is used to measure:
A) Association B) Central tendency C) Variability D) Forecasting
✅ Answer: A
📘 It measures linear association between two variables.
18. Fisher’s Ideal Index =
A) Laspeyres × Paasche B) C) L/P D) L + P
✅ Answer: B
📘 Geometric mean of Laspeyres and Paasche indices.
19. If the correlation coefficient is 0, the regression slope will be:
A) 0 B) 1 C) Undefined D) Infinite
✅ Answer: A
📘 Zero correlation → no linear relationship → slope = 0.
20. If data are highly spread out, the SD will be:
A) Low B) High C) Zero D) Negative
✅ Answer: B
📘 Greater dispersion → higher SD.
Section C: Sampling & Inference
21. Sampling error arises due to:
A) Mistakes in data B) Incomplete sampling C) Using sample instead of population D) Wrong hypothesis
✅ Answer: C
📘 Occurs because sample may not perfectly represent population.
22. In random sampling, every item has:
A) Equal chance B) Unequal chance C) No chance D) Weightage-based chance
✅ Answer: A
📘 Random → equal probability for all.
23. Stratified sampling is used when:
A) Population is homogeneous B) Population is heterogeneous C) Sample is large D) Randomness is not possible
✅ Answer: B
📘 Used to ensure all subgroups (strata) are represented.
24. Sampling distribution refers to:
A) Population distribution B) Distribution of a statistic over samples C) Normal curve D) Regression model
✅ Answer: B
📘 Sampling distribution = distribution of sample statistics like mean.
25. Standard Error =
A) B) C) D)
✅ Answer: A
📘 SE shows variability of sample mean.
26. Type I error =
A) Rejecting true H₀ B) Accepting false H₀ C) Accepting true H₀ D) Rejecting false H₀
✅ Answer: A
📘 α-error: reject a true null hypothesis.
27. Type II error =
A) Reject true H₀ B) Accept false H₀ C) Increase sample size D) Wrong distribution
✅ Answer: B
📘 β-error: fail to reject a false null hypothesis.
28. When population variance is unknown and n < 30, use:
A) z-test B) t-test C) F-test D) χ²-test
✅ Answer: B
📘 t-test handles small samples.
29. The χ² test is used for:
A) Comparing means B) Testing independence C) Regression D) Correlation
✅ Answer: B
📘 Chi-square → tests association or goodness of fit.
30. Power of a test =
A) 1 − α B) 1 − β C) α + β D) α × β
✅ Answer: B
📘 Power = probability of correctly rejecting false H₀.
Section D: Regression & Econometrics
31. Regression equation: — here “b” is:
A) Constant B) Slope coefficient C) Error D) Mean
✅ Answer: B
📘 b measures rate of change of Y per unit X.
32. In simple linear regression, number of parameters =
A) 1 B) 2 C) 3 D) Depends on variables
✅ Answer: B
📘 a (intercept) and b (slope).
33. BLUE stands for:
A) Best Linear Unbiased Estimator B) Basic Least Unbiased Equation C) Biased Linear Ultimate Estimation D) None
✅ Answer: A
📘 Gauss-Markov theorem: OLS estimators are BLUE.
34. OLS estimators are BLUE when:
A) Errors are correlated B) Homoscedasticity holds C) Mean of errors ≠ 0 D) Multicollinearity exists
✅ Answer: B
📘 Constant error variance (homoscedasticity) is one key assumption.
35. Multicollinearity refers to:
A) Correlation among independent variables B) Correlation between errors C) Correlation between X and u D) Serial correlation
✅ Answer: A
📘 Independent variables highly correlated → multicollinearity.
36. Heteroscedasticity means:
A) Constant variance B) Changing variance of errors C) Equal variance D) No variance
✅ Answer: B
📘 Non-constant variance → violates OLS assumption.
37. Autocorrelation occurs when:
A) Errors are independent B) Errors depend on past errors C) Variance constant D) Errors are random
✅ Answer: B
📘 Common in time series data.
38. The problem of simultaneous equations arises because:
A) Variables are exogenous B) Variables are interdependent C) Errors are normal D) Sample is small
✅ Answer: B
📘 Endogenous variables appear on both sides → simultaneity.
39. Recursive models:
A) Have feedback loops B) Have one-way causation C) Are non-identifiable D) Require IV estimation
✅ Answer: B
📘 Recursive → unidirectional, solvable by OLS.
40. Identification problem arises in:
A) Single equation B) Simultaneous equations C) Cross-section data D) Random sampling
✅ Answer: B
📘 Occurs when equations cannot be uniquely estimated.
41. Logit and Probit models are used when dependent variable is:
A) Continuous B) Binary C) Time series D) Multivariate
✅ Answer: B
📘 Discrete choice → 0/1 outcome.
42. Instrumental variables are used to correct:
A) Heteroscedasticity B) Endogeneity C) Autocorrelation D) Multicollinearity
✅ Answer: B
📘 IVs eliminate endogeneity bias.
43. Two-Stage Least Squares (2SLS) is used for:
A) Recursive models B) Non-recursive models C) OLS D) Binary models
✅ Answer: B
📘 2SLS → estimation of simultaneous equations.
Section E: Time Series & Miscellaneous
44. Components of time series include all except:
A) Trend B) Seasonal C) Cyclical D) Random Sampling
✅ Answer: D
📘 Random sampling isn’t a time series component.
45. The long-term movement in a time series is called:
A) Trend B) Seasonal variation C) Cycle D) Random
✅ Answer: A
📘 Trend shows overall direction.
46. Seasonal variations repeat:
A) Monthly B) Annually C) Daily D) Randomly
✅ Answer: B
📘 Seasonal → same pattern every year.
47. Stationary time series has:
A) Changing mean B) Constant mean and variance C) Random trend D) Increasing variance
✅ Answer: B
📘 Stationarity → constant mean, variance, covariance.
48. ARIMA models are used for:
A) Regression B) Forecasting time series C) Sampling D) Testing hypotheses
✅ Answer: B
📘 ARIMA = AutoRegressive Integrated Moving Average → forecasting.
49. Autocorrelation refers to:
A) Correlation between different variables B) Correlation between current and past values C) Randomness D) Error-free data
✅ Answer: B
📘 Measures serial dependence in time series.
50. Durbin-Watson test is used to detect:
A) Heteroscedasticity B) Multicollinearity C) Autocorrelation D) Nonlinearity
✅ Answer: C
📘 DW statistic → tests autocorrelation in regression residuals.