STOCHASTIC MODELS TEST QUESTIONS AND VERIFIED
ANSWERS
What is a stochastic model? - ANSWER Models that include
randomness or an unpredictable state.
How is "random" defined in statistics? - ANSWER All possible outcomes
are equally likely.
How is "random" defined in physics? - ANSWER A system or function
that is essentially unpredictable at a fundamental level.
What is the Gambler's Fallacy? - ANSWER The belief that the chances
of something happening with a fixed probability become higher or lower
as the process is repeated. Example: "we've had 4 heads in a row, it's
bound to come up tails next time"
Why doesn't random imply unpredictable? - ANSWER Even random
events may have probabilities associated with them - maybe we can't
predict H or T for one coin toss, but we can say something about what is
likely to happen from 100 coin tosses
What is the Infinite Monkey Theorem? - ANSWER A proposition that a
monkey typing randomly on a typewriter with infinite time, will eventually
produce a particular text, such as Hamlet or even the complete works of
Shakespeare.
Why do we study randomness in Biology? - ANSWER We can learn
something about biology by
treating some processes as at least partly
random
If there is randomness is biology, what is the point of modeling? -
ANSWER Even random event have probabilities associated with them.
We may not be able to predict an individual event, but we make
predictions in aggregate.
, How do computers simulate randomness? - ANSWER Programs called
Random Number Generators. Mersenne Twister is the current favorite of
programmers
Give an example of a fundamentally unpredictable system in physics. -
ANSWER Radioactive decay.
Cannot predict the likelihood of an 1 atom decaying, but can predict the
chances of a large quantity of atoms decaying.
What does RNG stand for? - ANSWER Random Number Generator
What is a Random Number Generator? - ANSWER A program that
creates a uniform deviates
What is uniform deviates? - ANSWER Numbers within some range for
which every number has the equal likelihood of appearing. Produces a
pseudorandom list of numbers.
What is a recursive equation? - ANSWER An iterative equation where
the answer is inserted into the same equation for the next answer.
Example: x2 = x1+1; x1 = x2, repeat.
What does "mod" stand for? - ANSWER Modulus operator
What is a modulus operator? - ANSWER remainder after simple division
Eg: 5/3 = 1 mod 2
What is a seed? - ANSWER The starting point in a RNG sequence.
What happens if you enter the same seed in an RNG? - ANSWER You
will always get the same sequence of numbers.
How does a RNG work? - ANSWER An equation that creates a
sequence based upon previous values.
Give an example of an RNG equation - ANSWER I(j+1) = (aIj +c) mod
m
ANSWERS
What is a stochastic model? - ANSWER Models that include
randomness or an unpredictable state.
How is "random" defined in statistics? - ANSWER All possible outcomes
are equally likely.
How is "random" defined in physics? - ANSWER A system or function
that is essentially unpredictable at a fundamental level.
What is the Gambler's Fallacy? - ANSWER The belief that the chances
of something happening with a fixed probability become higher or lower
as the process is repeated. Example: "we've had 4 heads in a row, it's
bound to come up tails next time"
Why doesn't random imply unpredictable? - ANSWER Even random
events may have probabilities associated with them - maybe we can't
predict H or T for one coin toss, but we can say something about what is
likely to happen from 100 coin tosses
What is the Infinite Monkey Theorem? - ANSWER A proposition that a
monkey typing randomly on a typewriter with infinite time, will eventually
produce a particular text, such as Hamlet or even the complete works of
Shakespeare.
Why do we study randomness in Biology? - ANSWER We can learn
something about biology by
treating some processes as at least partly
random
If there is randomness is biology, what is the point of modeling? -
ANSWER Even random event have probabilities associated with them.
We may not be able to predict an individual event, but we make
predictions in aggregate.
, How do computers simulate randomness? - ANSWER Programs called
Random Number Generators. Mersenne Twister is the current favorite of
programmers
Give an example of a fundamentally unpredictable system in physics. -
ANSWER Radioactive decay.
Cannot predict the likelihood of an 1 atom decaying, but can predict the
chances of a large quantity of atoms decaying.
What does RNG stand for? - ANSWER Random Number Generator
What is a Random Number Generator? - ANSWER A program that
creates a uniform deviates
What is uniform deviates? - ANSWER Numbers within some range for
which every number has the equal likelihood of appearing. Produces a
pseudorandom list of numbers.
What is a recursive equation? - ANSWER An iterative equation where
the answer is inserted into the same equation for the next answer.
Example: x2 = x1+1; x1 = x2, repeat.
What does "mod" stand for? - ANSWER Modulus operator
What is a modulus operator? - ANSWER remainder after simple division
Eg: 5/3 = 1 mod 2
What is a seed? - ANSWER The starting point in a RNG sequence.
What happens if you enter the same seed in an RNG? - ANSWER You
will always get the same sequence of numbers.
How does a RNG work? - ANSWER An equation that creates a
sequence based upon previous values.
Give an example of an RNG equation - ANSWER I(j+1) = (aIj +c) mod
m
