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The interview was conducted over Zoom video conference with 2 professors present. After the introductions, the following problems were asked from my selected topics – 

  • Probability theory and Discrete Mathematics. 

 

Professor 1 on Probability Theory ( Time: 20 mins including introductions)

  • Do you know what is a random variable?
  • Can you define it precisely? 
  • Now suppose you have a biased coin with the probability of a Heads being $p$ and the probability of a Tails being $(1-p)$ . How do you mathematically write the random variable for this?
  • Now suppose we are doing an experiment where we toss the same coin $N$ times. What is the sample space of this? 
  • What do you mean when you say Binomial distribution? 
  • Can you find the expected value of heads for above problem ($N$ tosses of the given biased coin)?
  • Okay, do the derivation.
  • Is there any other method to find it? 
  • Why do you say that you can add expected value of Bernoulli random variables?
  • Do the experiments need to be independent (for us to be able to add them to get the expected value)?
  • Calculate the expected value via the second method.

 

Professor 2 on Discrete Maths (Time: 15 mins)

  1. You are given $n$ vertices. Each pair of vertices $(v1, v2)$ are connected via an undirected edge. How many edges will be in the graph if self loops are allowed? 
  1. Suppose there are $n$ vertices and $e$ edges in an undirected graph. Can you say anything about the sum of the degrees of the vertices?
  1. Suppose I tell you that $n$ is odd and each vertex has an odd degree, is it possible? Can you write the explanation.
  1. Write down $a^2 + b^2 + 2ab$ $<=$  $k*(a+b)^2$ on the paper. Here $a,b$ are non-negative real numbers. Can you say anything about $k$?
  1. Now change it to $a^2 + b^2 + 2ab$ $<=$  $k*(a^2+b^2)$ . Can you say anything about $k$?

 

Hints: https://gateoverflow.in/blog/10821/my-rough-work-during-the-interview-for-csa-research-iisc

posted Aug 18, 2020 in Interview Experience
edited Aug 28, 2020 by
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2 Comments

What was the verdict in the end? Were you selected for CSA?
Yes, I was. I decided not to pursue further education.
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