Question 1 a) Compute the Hessian of the function: f(x1,x2) = 7x{2 5x1x2 4x22. x1 362 b) Given the function f(x1,x2,x3, x4) = 2x1 + x2 + 3x3 + 4x4, such that = [x3 x 4 . Find . . a the derivative of f. ax Question 2 Let X = number of heads after a coin is ipped three times. X ~ Bin(3, 0.5). What is the probability of each of the different values of X? Question 3 The amount of time required to make a bank transaction follows an exponential distribution with parameter 1 = 0.02 per minute. Find the probability that a client will have to wait less than 3 minutes. Question 4 The marks of 1000 students in an examination follows a normal distribution with Mean 70 and standard deviation 5. Find the number of students whose marks will be: 1) between 65 and 75. 2) less than 65