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%EDU Question bank for Stochastic Processes and Advanced Mathematical Finance
\begin{topic}{Randomness}
\begin{question}{key words}
\name{Frequentist approach}
\qutext{ Assigning probability $ 1/2 $ to the event that a coin will land
heads and probability $ 1/2 $ to the event that a coin will land
tails is a mathematical model that summarizes our experience
with many coins. In the context of statistics, this is called
the \emph{what} to probability.}
\answer{(frequentist approach)}
\end{question}
\begin{question}{key words}
\name{Assigning probability as summary}
\qutext{Assigning probability $ 1/2 $ to the event that a coin will land
heads and probability $ 1/2 $ to the event that a coin will land
tails is a mathematical model that \emph{what}? with many coins.}
\answer{(summarizes our experience)}
\end{question}
\begin{question}{true false}
\name{Deterministic process}
\qutext{A coin flip is a deterministic physical process, subject to the
physical laws of motion.}
\true
\end{question}
\begin{question}{key words}
\name{Bands of initial conditions}
\qutext{A coin flip is a deterministic physical process, subject to the
physical laws of motion. For high
initial velocities there are very narrow bands of
\emph{what} determine the outcome of heads or tails.}
\answer{(initial conditions)}
\end{question}
\begin{question}{key words}
\name{Assignment of half and half}
\qutext{The assignment of probabilities $1∕2$
to heads and tails is actually a statement of the
\emph{what} of the initial conditions that
determine the outcome precisely.}
\answer{(measure)}
\end{question}
\begin{question}{key words}
\name{Market theory}
\qutext{The \emph{what} of asset prices claims that market prices
follow a random path, without any influence by past price
movements.}
\answer{(Random Walk Theory)}
\end{question}
\begin{question}{key words}
\name{Predicting the market}
\qutext{This [Random Walk]
theory says it is impossible to predict which direction the market
will move at any point, especially \emph{when}.}
\answer{in the (short term)}.
\end{question}
\begin{question}{key words}
\name{Postulating a distribution}
\qutext{More refined
versions of the random walk theory postulate a \emph{what}
for the market price movements. }
\answer{(probability distribution)}
\end{question}
\begin{question}{key words}
\name{Mimicing a coin flip}
\qutext{The random walk theory mimics the mathematical model of a
coin flip, substituting a \emph{what} of outcomes for the
ability to predict what will really happen.}
\answer{(probability distribution)}
\end{question}
\begin{question}{key words}
\name{Technical analysis}
\qutext{\emph{What} claims to predict security prices with
the assumption that market data, such as price, volume, and patterns
of past behavior predict future (usually short-term) market
trends.}
\answer{(Technical analysis)}
\end{question}
\begin{question}{true false}
\name{Simplest model}
\qutext{The simplest, most common, and in some ways most
fundamental example of a random process is stock market
prices.}
\false
\end{question}
\begin{question}{key words}
\name{Mathematical model}
\qutext{ To assign the probability $1∕2$ to the event that the coin
will land heads and probability $1∕2$ to the event that the coin
will land tails is a \emph{what} that summarizes our experience
with many coins. }
\answer{(mathematical model)}
\end{question}
\begin{question}{key words}
\name{Inability}
\qutext{The assignment of probabilities $1∕2$
to heads and tails is actually a statement
of our \emph{what} to measure the initial
conditions and the dynamics precisely.}
\answer{(inability)}
\end{question}
\begin{question}{true false}
\name{Precision in coin-flipping}
\qutext{True or False: It is
possible to construct a precise coin-flipping machine that can
flip many heads in a row by controlling the initial conditions
precisely.}
\true
\end{question}
\begin{question}{true false}
\name{Testing the random walk theory}
\qutext{Random walk theory does not yet have
predictions that can be tested against evidence.}
\false
\end{question}
\begin{question}{true false}
\name{Hawking's definition of a theory}
\qutext{The cosmologist
Stephen Hawking says in his book A Brief History of Time “A
theory is a good theory if it satisfies two requirements: it
must accurately describe a large class of observations on the
basis of a model that contains only a few arbitrary elements,
and it must make definite predictions about the results of
future observations.” True of False: The random walk theory of
markets does both.}
\true
\end{question}
\begin{question}{true false}
\name{True Randomness}
\qutext{True or False: True randomness does not exist. All of the
physical universe is deterministic, anything less is a mere
summary of our inability to completely describe the situation.}
\false
\end{question}
\begin{question}{key words}
\name{When numbers are not random}
\qutext{In algorithmic
complexity theory, a number is \textit{not} random if it is
\emph{what}?}
\answer{(computable)}
\end{question}
\begin{question}{key words}
\name{What makes a number computable}
\qutext{ Roughly, a computable number has a \emph{what} that
will generate its decimal digit expression.}
\answer{(algorithm)}
\end{question}
\begin{question}{true false}
\name{Irrational numbers}
\qutext{True of False: Irrational numbers, such as some square
roots, which have nonrepeating, nonterminating decimal
expansions are necessarily random, in the sense of algorithmic
complexity theory.}
\false
\end{question}
\end{topic}
\end{document}
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