Following questions were asked for Strategic Risk Management profile of Credit Suisse at IIT-Bombay.
1) Value of E[|X|] where X ~ Normal(0,1)
2) Choose 3 points on circumference of a circle. What is the probability that the center will lie in the triangle?
3) There are 2 men who want to meet between 5pm and 6pm. Assuming arrival time is uniform and random, calculate the probability that 2nd arriving person has to wait less than 10 mins
4) What is the expected number of tosses needed to get 2 consecutive heads?
5) You are given a 6-sided fair die. Calculate expected number of throws of dice to see all the faces (values 1,2...6) at least once.
6) Solve: dy/dx + xy = x*(y^2)
7) Solve: dy/dx + 3y = e^x
8) Calculate Sum(Var(pow(Xi,2))), i = 1 to N, Xi are independent.
9) Calculate Var(XY) where X ~ Uniform(0,1) and Y ~ Normal(0,1)
10) There are 3 bulbs in a room. If we switched on all of them. What is the total expected time till the room remains lit? Assume the "on" time for each bulb is an exponential random variable with λ=1 hour.
11) There are N coins. Probability of kth coin to land up a head is 1/(2k+1). We toss all the N coins, calculate the probability that we get odd number of heads.
12) Dart thrown land up uniformly and random at a distance from centre of a unit circle. Distance from center is in the range [0,1]. One who lands up farther from the center loses and the loser pays amount equal to distance from the centre. What is the expected pay?
13) Calculate E[f(x)], where x ~ N(0,1) (For some function f).
14) Given X ~ Uniform(-π/2, π/2). Find probability distribution of Y = tan(X).
15) f(x,y) = (x^2 - y^2) / (x^2 + y^2). Comment on continuity of the function at (0,0)
16) We do M trials. In each trial the result is a uniform RV in [0,1]. What is the minimum no of tosses needed to be 90% sure of getting a value in range [0.8, 0.9].
1) Value of E[|X|] where X ~ Normal(0,1)
2) Choose 3 points on circumference of a circle. What is the probability that the center will lie in the triangle?
3) There are 2 men who want to meet between 5pm and 6pm. Assuming arrival time is uniform and random, calculate the probability that 2nd arriving person has to wait less than 10 mins
4) What is the expected number of tosses needed to get 2 consecutive heads?
5) You are given a 6-sided fair die. Calculate expected number of throws of dice to see all the faces (values 1,2...6) at least once.
6) Solve: dy/dx + xy = x*(y^2)
7) Solve: dy/dx + 3y = e^x
8) Calculate Sum(Var(pow(Xi,2))), i = 1 to N, Xi are independent.
9) Calculate Var(XY) where X ~ Uniform(0,1) and Y ~ Normal(0,1)
10) There are 3 bulbs in a room. If we switched on all of them. What is the total expected time till the room remains lit? Assume the "on" time for each bulb is an exponential random variable with λ=1 hour.
11) There are N coins. Probability of kth coin to land up a head is 1/(2k+1). We toss all the N coins, calculate the probability that we get odd number of heads.
12) Dart thrown land up uniformly and random at a distance from centre of a unit circle. Distance from center is in the range [0,1]. One who lands up farther from the center loses and the loser pays amount equal to distance from the centre. What is the expected pay?
13) Calculate E[f(x)], where x ~ N(0,1) (For some function f).
14) Given X ~ Uniform(-π/2, π/2). Find probability distribution of Y = tan(X).
15) f(x,y) = (x^2 - y^2) / (x^2 + y^2). Comment on continuity of the function at (0,0)
16) We do M trials. In each trial the result is a uniform RV in [0,1]. What is the minimum no of tosses needed to be 90% sure of getting a value in range [0.8, 0.9].
