Probability, Statistics, and Applications

Perform the following experiment by writing a MATLAB program to simulate tossing a

fair coin. (You may want to use the MATLAB command

rand

or

randi

in order to

produce random outputs.) Simulate flipping the coin five times and observe the

number of heads. Then, repeat this experiment (that is, flipping the fair coin five times

and counting the number of heads) 10 times. Using the

equation

* in P

roblem

1,

determine the probability for

each of

k=0,1,2,3,4,5 heads. Based on this theoretical

result, what is the number of heads that is most probable for a single experiment? In

your 10 experiments which number of heads appeared most often? For 1000

repetitions of the experiment, what is the simulated probability of obtaining four heads

in five coin tosses? Compare your result to that obtained using the

equation

*.

(Problem

3 is an example of a Monte Carlo simulation, a computational simulation of a

random exp

eriment repeated many times to estimate the probability distribution of the

experimental outcomes. In this example, you performed the experiment 10 times and

then 1000 times. How many repetitions is “enough”? If you were performing such an

experiment in a

real

-world setting in which you did not know the theoretical

probability distribution before beginning the experiment, how might you determine

whether you have performed “enough” repetitions to uncover the true distribution?

[Andrew Janke]

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[Rik]

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