Multiple Choice Questions in Probability and Statistics with Answers pdf for the preparation of Banking, Finance, MBA, BBA, Mcom, Bcom exams.

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This article provides a comprehensive guide to the world of Probability and Statistics MCQs with answers. Here, you will find helpful resources that cover a wide range of topics in Probability and Statistics through well-crafted MCQs.

#### What is Probability and Statistics

Probability and statistics are two interrelated fields of study that deal with understanding and analyzing data. Probability refers to the likelihood or chance of an event occurring, while statistics involves the collection, analysis, interpretation, presentation, and organization of data.

These two areas of study are crucial in various fields such as business, finance, social sciences, engineering, medicine, and many others.

Probability is used to predict the chances of something happening or not happening based on past occurrences or patterns. It is often expressed as a percentage or a fraction ranging from 0 to 1.

Statistics help us make sense of data by using various methods such as regression analysis, hypothesis testing, sampling techniques and more. Through statistical analysis we can draw conclusions about populations based on samples taken from them.

In summary probability and statistics are powerful tools in helping us understand our world better through data-driven decision-making processes.

## MCQs in Probability and Statistics with Answers

1. The consistency and adequacy of an index number formula CANNOT be verified by which of the following?

a. Order reversal test

b. Factor reversal test

c. Time reversal test

d. Index reversal test

Answer: (d)

2. Time series is defined as the set of ordered pairs of observations taken at ___ points of time.

a. equal

b. successive

c. progressive

d. random

Answer: (b)

3. Time series analysis plays a vital role in business decision-making for which of the following?

a. Understanding of past behaviour

b. Planning future operations

c. Evaluating the performance

d. All the above

Answer: (d)

4. Which of the following is NOT among the elements of the time series?

a. secular Trend

b. regular variations

c. cyclical variations

d. seasonal variations

Answer: (b)

5. Which among the following is NOT among the phases of the business cycle?

a. decline

b. improvement

c. dispersion

d. Prosperity

Answer: (c)

6. Trend can be measured by which of the following?

a. Graphic or freehand curve fitting method

b. Method of Moving Averages

c. Method of Semi-Averages

d. All the above

Answer: (d)

7. Seasonal Trend can be measured by which of the following?

a. Residual method

b. Harmonic Analysis

c. Link Relative Method

d. Direct percentage method

Answer: (c)

8. Which of the following statement is Not true regarding Sampling?

a. Saving of time.

b. Reduced cost of the survey

c. Non-precision of results

d. Adaptability

Answer: (c)

9. Which of the following is not among the principles of sampling theory?

a. Principle of optimization

b. Principle of persistence of small numbers

c. Principle of validity

d. Law of statistical equality

Answer: (d)

10. The principle of ___ aims at obtaining a desired level of efficiency at minimum cost or obtaining maximum possible efficiency with a given level of cost.

a. Validity

b. Optimisation

c. Persistence of Small Numbers

d. Inertia of Large Numbers

Answer: (b)

11. Compensatory errors are also known as which of the following?

a. Biased errors

b. Compiling errors

c. unbiased errors

d. Publication errors

Answer: (c)

12. Which of the following is not a type of probability sampling?

a. Judgment Sampling

b. Multi-stage Sampling

c. Systematic Sampling

d. Simple Random Sampling

Answer: (a)

13. Hypothesis testing is the opinion about the population parameter that may or may not be in the ___ interval derived from the sample.

a. regular

b. confidence

c. equal

d. successive

Answer: (b)

14. ___ test is the test of any statistical hypothesis where the Alternative hypothesis is written with the symbol “≠”.

a. One-tailed

b. Two-tailed

c. Right-Tailed

d. Left-Tailed

Answer: (b)

15. Cyclical variations can be measured by which of the following?

a. Direct percentage method

b. Ratio–to–trend Method

c. Method of Simple averages

d. Ratio-to-moving Average Method

Answer: (a)

16. Which of the following principles states that “other things being equal, as the sample size increases, the results tend to be more reliable and accurate”?

a. Principle of Validity

b. Principle of Inertia of Large Numbers

c. Principle of Optimisation

d. Principle of Persistence of Small Numbers

Answer: (b)

17. A die is tossed once. Let Y be an event such that Y = {odd number occurs on the bottom}. What is the number of favourable outcomes of Y?

a. 1

b. 2

c. 3

d. 4

Answer: (c)

18. A coin is tossed 6 times. Let T be an event such that T = {More tails than heads showed}. What is the number of favourable outcomes of T?

a. 14

b. 22

c. 26

d. None of these

Answer: (b)

19. What is the numerical value of the exhaustive number of cases if you throw a dice 5 times?

a. 1296

b. 4616

c. 7776

d. 9636

Answer: (c)

20. ”Number of children’ measurement is which of the following?

a. Qualitative random variable

b. Discrete random variable

c. Continuous random variable

d. Nominal random variable

Answer: (b)

21. A random variable X has the density function : f(x) =

1/4 * kx^4 when -2<=x<=2

f(x) = 0 elsewhere.

What is the value of k?

a. 3/28

b. 9/32

c. 7/18

d. 5/16

Answer: (d)

22. A random variable y has p.m.f. f(y) as f(y) = y/9, y ϵ M where M = (-3, 0, 3). Then what is the value of E(y)?

a. 2

b. 3

c. 4

d. 5

Answer: (a)

23. From a bag containing two 5 rupee coins and two 1 rupee coins, a person is asked to draw 2 coins at random. Find the value of expectation in rupees.

a. 2

b. 3

c. 4

d. 6

Answer: (b)

24. The pdf for the score for a randomly selected student is

X = 0; f(X) = 2

X = 1; f(X) = 5

What is the moment generating function of the random variable X?

a. 10et

b. et+10

c. 2et+5

d. 5et+2

Answer: (d)

25. Calculate the fourth moment about origin with the help of mgf of probability density function f(x) = e-x, 0 <= x < ∞.

a. 16

b. 20

c. 24

d. 30

Answer: (c)