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].
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