Problem 1

A function plot is shown below:

The function is given by:

 a) 
 b) 
 c) 
 d) 

Problem 2

Which of the following statistical measures can be measured geometrically (in a Cartesian and/or polar coordinates):

a)   standard deviation
b)   variance
c)   mean
d)   standard error

Explain your answer in as precise a way as you can.

Problem 3

Eigenvectors and eigenvalues are associated with:

a) correlation matrix
b) variance covariance matrix
c) both (a) and (b)
d) none of the above

Problem 4

You are living in the 16 ^th century with Galileo. You are told at school that a heavy body falls faster than a light body when dropped from the Tower of Pisa . So you start to wonder: if you have a heavy body, H, say, an iron ball, then it will fall faster than a lighter body, L, say, a feather ball. However, you are imprisoned in a room for a long period of time and hence you are unable to carry out an experiment to prove or dis-prove the above scientific theory. But you can think.

Carry out a thought experiment, in not more than 4 to 5 lines to either accept or challenge the above theory.

Problem 5

A market maker is a financial institution that stands ready during the entire trading day with a firm bid and ask price. All traders (working in brokerage and securities houses) buy from and sell to the market maker(s). At time a market maker sets bid (buy) and ask (sell) prices of a certain stock as and respectively. An informed trader (with market knowledge and intelligence) knows the true (intrinsic/fundamental/fair) value of the stock as . Which of the following statements is FALSE:

(a) the trader will place a buy or a sell order with equal probability and no order (to       trade) with some probability;
(b) The trader will place no order to trade if
(c) The trader will place an order to buy if and an order to sell if
(d) All the above statements are FALSE;

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