Simulating
Experiments
ntroduction to Random Variable
Simulation
The imitation of chance
behavior based on a
model to accurately
reflects the experiment
under consideration
Steps in simulating
experiments:
1. State the problem clearly
2. Define the key components
3. State the underlying assumptions
4. Select a model to generate the outcomes for a key
components
5. Define and conduct a trial
6. Record the observation of interest
7. Repeats steps 5 and 6 at a large number of times
8. Summarize the information and draw conclusions
Example: A run of three in tossing a coin
10x
Step 1
State the problem: Toss a coin 10 times. What is
the likelihood of a run of at least 3 consecutive
heads or 3 consecutive tails
Step 2
State the assumption: There are 2.
1. A head or a tail is equally likely to occur
2. Tosses are independent of each other. (what
happens on the first toss will not influence the next
toss)
StepAssign
3
digits to represent outcomes Using
random number table on Table B we assign:
1. One digit simulate one toss of the coin
2. Odd represents heads, even digits represents
tails
Step 4
Simulate many repetition: looking at 10
consecutive digits on table B, simulate one
repetition. Read as many groups of 10 from the
table to simulate many repetitions:
Let’s use line 101 of table B for our first three rounds of
simulation.
D 1 9 2 2 3
9 5 0 3 4
0 5 7 5 6
2 8 7 1 3
9 6 4 0 9
1 2 5 3 1
H H T T H
H H T H T
T H H H T
T T H H H
H T T T H
H T H H H
H/T
First round: Yes
2nd round: Yes
3rd round: Yes
22 more rounds were
added and out of the 25
rounds. 23 of them did
have a run of three
Step 5
State your Conclusion: We estimate the
probability of a run of size 3 by the proportion
Estimated probability= 23/25= 0.92
There is a 92% chance of getting a run of three when
you toss a coin 10 times.
True mean: 0.826
Difference between dependent and independent
trial
Independent trial: the number of trials
has no effect on the succeeding trial
Example: tossing a die, flipping a coin,
drawing a card
Dependent trial: shooting 10 free throws
in a basketball. Getting an A on the first
quiz.
Shooting free throws
Lisa makes 70% of her free throws in a long
season. In a tournament game she shoots 5
free throws late in the game and misses 3 of
them. The fans think she was nervous, but
the misses may simply be chance. You will
shed some light by estimating a probability.
answer Shooting Free Throws:
Single random digit will simulate a shot, with 0-6
representing the basket made and 7,8,9
representing the miss.
5 consecutive digits using Table 5 can simulate 5
shots.
D
m
9 6 7 4 6
X
X
1 2 1 4 9
X
3 7 8 2 3
X X
7 1 8 6 8
X
X
x
After 46 more repetitions:
Number of misses
0
1
2
3
4
5
frequency
6
15
18
10
1
0
The relative frequency of missing three or more shots in
five attempts is 11/50= 0.22