FYCS DM Stats Sample Questions

Discrete Mathematics
Unit – I Sample Questions
a) Define subset, power set, proper subset, Cartesian product, relation, function, degree of
recurrence relation, one-one function, onto function, bijection.
b) State the recurrence relation for Fibonacci series problem.
c) State the recurrence relation for towers of Hanoi problem. Given value of n, find number of
moves required.
d) State the recurrence relation for finding the number of regions (Intersection of lines in a
plane). Given value of n, find the number of regions required.
e) Identifying function or not, Counting number of functions from set A to B, Counting number
of one to one functions possible from set A to set B, identifying one-one, onto function or not.
f) Identifying ordered pair belongs to relation or not, checking for reflexive, symmetric,
transitive relations, Counting number of relations from set A to B, Counting number of
relations on set A, Counting number of reflexive relations possible on set A, Smallest possible
reflexive relation on set A?
g) All questions from lecture notes and Practice Questions.
h) All quiz questions of Mathematical logic.
Unit – II Sample Questions
Counting Principles, Permutations & Combinations: Kenneth Rosen Book
Languages, Grammars & Machines: Lecture Notes
Statement of Product Rule and Sum Rule.
When to use product rule? When to use sum rule?
Unit – III Sample Questions
Refer PPT
Statistics & R – I
Unit – 1 Sample Questions:
Q.1. Do hands on writing practice of all formulas (all units) at least twice.
Q.2. Define quartile, decile and percentile.
Q.3. Define exclusive and inclusive class interval. State the difference between them.
Q.4. List any three measures of central tendency.
Q.5. List any three measures of variation.
Q.6. State the characteristics for an ideal measure of central tendency.
Q.7. State the characteristics for an ideal measure of variation.
Q.8. Mean deviation practice questions: Mean Deviation (mathsisfun.com)
Q.9. Standard deviation: Standard Deviation and Variance (mathsisfun.com)

Q.10. If 5, 8, 6, and 2 occur with frequencies 3, 2, 4, and 1, respectively, the arithmetic mean is ____.
(Ans. 5.7)
Q.11. The following is the marks obtained by 140 students in a college. Find the median class. (Ans.
49.5-59.5)
Unit – II Sample Questions:
Q.1. Do hands on writing practice of all formulas (all units) at least twice.
Q.2. Define correlation, Define regression.
Q.3. State the two lines of regression. Which line of regression to use in a given scenario?
Q.4. State the difference between the correlation and regression with suitable example.
Q.5. State the properties of covariance.
Q.6. State the properties of correlation coefficient.
State the properties of regression coefficients.
Q.7. Marks given by two judges to eight contestants in the elocution competition are given in the
table.
a) Find the ranks of A.

b) Find the ranks of B.
c) Find the sum of squares of differences of ranks.
Q.8. The coefficient of correlation between two variables X and Y is 0.48. The covariance is 36 and
variance of X is 16. Find standard deviation of Y. (Ans. 18.75)
Q.9. From the following data compute the coefficient of correlation between X and Y. (Ans. 0.06)
Q.10. mean(x) = 53, mean(y) = 28, byx = -1.5, bxy = -0.2 Find r. (Ans. -0.5477)
Q.11. From two regression equations, 4y = 9x + 15 and 25x = 6y + 7 Find mean(x). (Ans. 2.565)
Q.12. From two regression equations, 4y = 9x + 15 and 25x = 6y + 7 Find r. (Ans. 0.7348)
Unit - III
Refer Quiz on Probability, PDF of Practice questions, Lecture Notes
Study the examples on how to identify random variable as Discrete or Continuous.
State the properties of probability mass function.
- Mention the point-wise answer (2-3 points); Sum of probabilities of all events should be
equal to one, Probability of every event should lie between 0 and 1; one example of pmf.
Define cumulative distribution function of discrete random variable X.
- c.d.f. of random variable X is: F(X) = P(X ≤ x) explain this with one example.
State the condition for independent events.
Difference between mutually exclusive events and independent events.
Also, practice examples on discrete random variables
R Programming fundamentals like:
- R function to import CSV files.

- R function that returns a logical vector with TRUE in element locations that contain missing
values.
- Find range of x <- c(2, 7, 1, -17, Inf, 35, 21, 7, NA) in R by dropping NA values.
- b<-c(1+8i, 9+3i) What will class(b) give?
- To find correlation between two variables X and Y, R function used is ____.
- To find covariance between two variables X and Y, R function used is ____.
- R functions for mean, median.
- If I have two vectors x <- c(1,3, 5) and y <- c(3, 2, 10), what is produced by the expression
cbind(x, y)?
- Factors are used to represent ____ data
- Etc.
Note:
1) Do hands on writing practice of all formulas (all units) at least twice. PDFs of formulas of all
units is already shared with you all.
2) Manage your time properly where the calculation steps are required. Keep a practice of
completing calculation quickly and accurately. Do not spend too much time on a single
problem.
3) Be very specific and to the point in answering the descriptive questions. Mention examples
where required.
Theory Answers References
Properties of covariance:
a) Cov(X, Y) = Cov(Y, X)
b) Cov(X, C) = 0 where C is any constant
c) Covariance may be positive, negative or zero.
d) Cov(X, X) = Var(X)
e) Covariance is invariant to the change of origin but is affected by the change of scale.
Properties of correlation coefficient:
a) Corr(X, Y) = Corr(Y, X)
b) Correlation coefficient does not change in its magnitude under the change of origin and
scale.
c) Corr(X, X)=1
d) -1 ≤ r ≤ 1
Scatter diagram is the graphical method to study correlation.

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Discrete Mathematics

Unit – I Sample Questions

Unit – II Sample Questions

Counting Principles, Permutations & Combinations: Kenneth Rosen Book

Languages, Grammars & Machines: Lecture Notes

Statement of Product Rule and Sum Rule.

When to use product rule? When to use sum rule?

Unit – III Sample Questions

Unit – 1 Sample Questions:

Q.2. Define quartile, decile and percentile.

Q.4. List any three measures of central tendency.

Q.5. List any three measures of variation.

Q.6. State the characteristics for an ideal measure of central tendency.

Q.7. State the characteristics for an ideal measure of variation.

Q.8. Mean deviation practice questions: Mean Deviation (mathsisfun.com)

Q.9. Standard deviation: Standard Deviation and Variance (mathsisfun.com)

Unit – II Sample Questions:

Q.2. Define correlation, Define regression.

Q.5. State the properties of covariance.

Q.6. State the properties of correlation coefficient.

State the properties of regression coefficients.

a) Find the ranks of A.

Refer Quiz on Probability, PDF of Practice questions, Lecture Notes

Study the examples on how to identify random variable as Discrete or Continuous.

State the properties of probability mass function.

Define cumulative distribution function of discrete random variable X.

State the condition for independent events.

Difference between mutually exclusive events and independent events.

Also, practice examples on discrete random variables

R Programming fundamentals like:

- R function to import CSV files.

Theory Answers References

Scatter diagram is the graphical method to study correlation.

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