Skip watching entire videos - get the full transcript, search for keywords, and copy with one click.
Share:
Video Transcript
Video Summary
Summary
Core Theme
Simulations are a powerful statistical tool used to estimate probabilities that are difficult or impossible to calculate directly, by imitating real-world scenarios through various methods like physical objects or computational tools.
Mind Map
Click to expand
Click to explore the full interactive mind map • Zoom, pan, and navigate
simulations are an incredibly powerful
tool for calculating probabilities and
they're used a lot when the
probabilities are either too tedious or
time-consuming or difficult to find by hands
hands
um there's you see them everywhere in
statistics especially because nowadays
you can just have a computer calculate
it for you and give you the answer
without having to design it and take the
time to do it yourself technology makes
doing simulations so easy um when I was
working on my master's in statistics my
big end of master's project that I was
doing I had to calculate a bunch of
probabilities and figure out the
theoretical side of things but then to
make sure I had actually done my work
correctly I ran it through a computer
simulation so they have all sorts of
uses and they're really really valuable
in the concepts in the realm of
statistics and in probability so what
actually is a simulation good definition
of a simulation is an imitation of a
probability essentially you try to
recreate whatever it is you're studying
and use your recreated model to figure
out the probability where it would be
like either impractical or tinea sir
impossible to do it in real life
we've done several examples of
simulations already in this class and
we'll do a lot more on before the end of
the year on the very first day of school
we did that pilot discrimination example
that was an example of a simulation
I didn't bring 15 pilots into our
classroom and start picking them I used
like a little bag with the color tubes
in it and we picked the estimated
probability that way so you can use some
other sort of objects to represent your
situation where it's easier to handle
you can also use a computer or
technology just in our last lesson we
did that thing with the textbook slash
baby um thing
five point one a that was a simulation
and we've done others over the course
this semester already as well very
common concepts so let's talk about how
you actually go about designing a
simulation yourself in real life you're
going to use a you're gonna use the
technology computers probably just gonna
do it for you but even though that's
true you need to have an appreciation
for what it is the computer is doing I
understand how to like a simulation may
work even though I don't want to do it myself
myself
I can at least use that information to
help me when it gives me my results you
want to be able to appreciate what is
going on behind the scenes so ap
statistics makes you guys design nice
basic simulations or do small-scale ones
by hand to give you an idea of how they
work even though in real life you would
probably just use a computer and do a
hundred thousand trials so the four-step
process that you'll use for this kind of
problem is a four step profit process
I've referenced before it's our books
then and we do it second semester too
but the four steps are States plan do
and conclude and it talks about what
each of these steps are gonna be
basically you set up your problem you
plan out how one trial is gonna work in
lots of detail then you do it a lot of
times and you estimate the probability
so we'll walk through an example and you
guys will see how that works but this
basically when you write these out
you're gonna have to give lots and lots
of very specific detail so they know
that you really understand what's going
on so first thing we're gonna do is look
at the textbook example that we did just
last time I think with this one well I
will talk through it and I'll just have
the answer flash up there so you guys
can see what's going on first thing you
would do is state what probability
you're trying to find kind of set the
stage so I would talk about for our
textbook problems what's the probability
that if you have four people who all
randomly shuffled their textbooks in
grab one that none of them get their
same textbook back you're basically just
setting the stage for your problem then
in the plan step what you would do is
you would talked in a lot a lot of the
about how you're gonna work your
simulation how does a trial work it
could be where we do something with
random numbers we use like randant on
our calculator we could use a random
table we could actually put index cards
and deal them out and that might not be
a bad way to do it so I think for this
one what I'm gonna say and what I'll end
up writing about in two seconds is I'm
gonna have four pieces of paper one two
three four and then what I'm gonna do is
I'm gonna have four smaller index cards
also numbered one two three four my four
pieces of paper will be out what I'm
gonna do is I'm gonna shuffle those four
index cards up little index cards and
deal them facedown on each piece of
paper and I'm gonna see if any of them
match so I do a trial where I dish out a
card to all four I see if any of them
matched and if they do or they don't I
keep track of that so I write down if
there were zero matches or if there was
something else going on okay that would
be like one trial and then I would do
that same thing lots of times over and
over deal at four deal out for a lot for
and after I do it like a hundred a
thousand ten thousand times I would look
at what proportion of the time I got
zero matches so I think the number of
zeros out of the total number of trials
and that's basically how that work so
I'll put up an answer that gives
sufficient detail for my explanation
right there you very easily could have
done this a different way with like
randant or something like that and
that's totally fine but I'll do the
index card way when I write this one up
alright so you can see below it's kind
of a lots you have to write out for one
of these people don't usually enjoy
doing simulation style questions
thinking about them isn't so bad but
writing them out is a little bit tedious
but in the blue I have my original
question purple here is talking in
detail about how one trial would work
the orange is really easy you just say
you repeat many times and then in theory
you would actually do some trials um I
just remembered from our last video that
they probably was around 38 so I made
this up I didn't do 100 trials myself in
like practice like for a quiz or
something you would probably use
something like 5 trials or 10 trials and
it'll tell you how many to do will get
practice with that towards the end
this video but you just do your process
and then you estimate the probability
that there wasn't before that's how you
set up a simulation so this one I think
wasn't that bad to write out like you
can kind of just logic it and be like
okay yeah four people four books and
then you can make something that works
pretty well but naturally probability
can be tougher to wrap your head around
depending on how complicated the
situation is that you're talking about
so we have a brand new problem right
here there's a basketball player and
apparently that player is considered a
very streak need by the announcer they
justify saying that their streak lead by
saying wow they make a lot of their
shots in a row um and in this most
recent game the player took 30 shots and
had a streak of seven in a row where
they made them okay so with sports
examples in general you have to make an
assumption that's maybe or maybe not
realistic which is that like one shot is
independence of next so if you air ball
on your first shot that's not gonna get
in your head and influence how you do on
your next shot each shot is considered
independent that may or may not be
realistic for certain players but it's
usually considered an okay assumption to
make so basically this announcer is
saying this guy is a streaky shooter
because in 30 shots he got seven in a
row and that seems like a lot that seems
like a big deal getting seven and rip
the player makes 47% of their shots
overall but that's not like that's not
why they're saying the personal streets
they're streaky because they made seven
out of a set of thirty so we want to
figure out is that a big deal
could you be a forty seven percent sugar
and get seven in a row in a set of
thirty pretty easily or is that kind of
hard to do so we have to think and wrap
her head around how we would like
recreate this tougher situation with a
simulation so maybe even pause me it'd
be good if you did on to think about
like what you would do and I'll give you
some thoughts or ideas on this so the
first thing is that you need to have
thirty trials in whatever you're doing
so if you're using randoms if you're
gonna like do I don't know
something with coin a coin or whatever a
die you need to roll 30 times for one
trial so you have to have 30 shots
representing just for one trial and then
we would do that a bunch of times if you
said something like flip a coin see if
it's heads or tails from making a shot
that wouldn't work out because they're a
47% shooter if they were a 50 percent
shooter they'd be perfect we can just
very easily flip quarters and look at
like common unit heads in row we got but
because this probability is a little bit
more off-the-wall the best thing to do
here is to use some sort of random
number generator and do it that way
instead it's gonna make it so you can
actually get that 47 percent that you
need so again what I'm gonna do here is
talk you through what I would do and
then after that I'll write up a nicer
explanation for you guys to copy down so
you can see what a full credit answer
would look like for this problem I
wanted you randint on the calculator and
when you do ran dints your digits don't
need to be the same size so I'm gonna go
randant and i'm gonna do one through a
hundred right here I'm basically trying
to recreate a forty-seven percent
shooter so what I would do if I do a
randant one through a hundred is I would
get look and let's say the number is one
through forty-seven means that you made
the shot so I'll put yes for that and
then I would have 48 all the way up to a
hundred meaning that they missed the
shots okay now do you have to have the
labels the same as me
no if you did 1 through 53 you miss and
then the rest of them make that's fine
too as long as it appropriately
represents the problem so what I would
need to do now once I have these labels
right here is I would hit randant
and I would do that 30 times oh I got 30
i got 37 for my first number that's a
make oh I got 42 that's a make oh I got
74 that's a miss oh I got a 91 miss etc
and you would do that until you have 30
trials altogether so you would do that
for all 30 of these after you get your
30 actually before I get to that let's
think really quick about whether
kids would be okay do we want repeated
numbers to be allowed so like if I get
the number one for my first trial could
I get the number one again the answer is
yes I would want to be able to repeat a
number because these aren't actual like
objects that I'm saying these are meant
to represent probability and if I take
out the number one well then it's not a
47% chance I'll make it any more you're
messing with the probabilities so you
would want to allow repeats and I'll
talk about that when I write my answer
so anyway you get your 30 trials right
here a lot of times we do this in class
with randant and then we go around the
room because everybody has a different
trial after you do this though what you
care about is not how many you made we
just want to see how likely it is that
you get seven in the row that's the
probability that we cared about so I
would look through all my yeses and noes
right here and see if I got seven yeses
in a row at some point in my process if
I did then that's a success for my trial
I got it at seven in a row and if I
didn't be enough after you do that a
bunch of times you would just count the
proportion or find the proportion of
times you've got seven or more and then
you would calculate a probability so I
will write up a little explanation of
what that looks like okay so here is a
long kind of written out answer here
that would get full credit for a problem
like this again I know it's not fun to
write this down and it's like these
problems take a little bit of time to
write them out but you have to be very
very specific in what you say
I basically recap everything we talked
about right here and I made sure I
mentioned that repeats were okay for
this problem oh and then I just made up
a probability usually when I do this in
class we get something pretty low like
nobody or one person gets seven or more
in a row so I set out of twenty people
in class because like what we would have
done is had each of us into it and then
we'd get our trials that way because it
takes a long time to do thirty numbers
that's just for one trial so yeah you
get a probability and it would be fine
so simulations the trick is mostly just
wrapping your head around how to design
the problem and then taking the time to
actually write the thing outs we're
going to talk about one more example in
this way
and we're gonna do it with a random
number table which we've used before
back in our first chapter when we talked
about chapter four we were talking about
like random assignment and that sort of thing
thing
when you use a table you need to make
sure Green doesn't show up very well
let's change colors here so make sure
all labels are the same size so we've
talked about like if we were doing that
same problem we just did we could go
zero one two I guess if we did here oh
one Oh that'd be weird I'd have to go
zero zero one to 100 or I can go zero
zero zero two zero nine nine either of
these would have been okay since I had a
hundred numbers I need three digits of
peace that I would look at oh and also
talk about rejected numbers so you gotta
talk about any numbers you're not going
to use and we'll see how that plays out
in our next example so those are just
two things to watch out for here this
one I want to do a shorthand for so I'm
not gonna make you write the whole thing
again hopefully you wrote the last two
out we'll just talk like highlights and
actually work out the simulation on the
table on the next page so I want a
sample of size six and I have 60 seniors
and I have thirty juniors so I put
everybody's name on a paper I put in a
bag and I pull amounts but somebody
pointed out well you should do a
stratified sample instead and make it
representative to that population
weights because I have way more I've
doubled the seniors that I viewed unions
but I just shuffled all the papers up so
I don't really want to have to separate
them and then put 60 and 30 if I did
have 60 and 30 separate it would be kind
of easy I pick four from here two from
here but they're all in one bag and I
don't want to fix that so what I'm gonna
do is I'm gonna pick and if I run out
like I get too many seniors I'll just
throw the number out I'll pick something
else don't keep going like that until I
actually gets my sample so we are going
to design a simulation using a table to
estimate the probability that it must
take eight or more
to get for seniors to juniors so I'm
going to show you how this process works
but we're not actually to do a ton of
trials with this year that's the basic
set so I need eight or more picks is the
probability I care about to get 14 years
to juniors out of this so I'm not
writing out the whole thing let's just
talk labels and what I would need to do
first step is assign labels and get the
things set up well actually first step
is say the probability what's the
probability that in a set of 60 senior
started Union just takes a term or picks
to get this just restating that next
thing you do is get your labels ready to
go so I have 90 people who are in this
problem right here
so if I have 90 of them I got to do two
digits I'm gonna go I like starting with
zero zero that way I don't forget to
like rule it out later
so zero zero through fifty nine are
gonna equal seniors and then that would
make number sixty through 89 juniors one
of the more common errors on this is
people doing like the wrong meds on that
saying 0 to 60 which would be actually
61 numbers so just make sure you're
careful with that so if I was writing
this out I would say a sign unique
number to each students and I've got my
labels right here so now what I'm gonna
do in this problem
do I want repeats I do not because that
would be taking the same person twice
for my committee here so I would need to
make sure that I reject two repeats and
I also need to make sure that I reject
the numbers nine year through ninety
nine those don't correspond to an
individual so let me just walk through
how that work and show you a trial right
here my first number is a 19 so if I do
this usually when they give you a table
like this they want you to mark it up
and show what you did number 19
represents a senior so I have a senior
then I have 22 another senior that I
have thirty-nine another senior 50 is
another senior I was supposed to have
four seniors so now I'm gonna shut it
down anymore
seniors that I get I would want to throw
away 34 is another senior I think I'm on
34 it's kind of hard to see you right
here yeah 34 is a senior so they're out
five is a senior so they're out double
zero five I have 75 that's a junior and
I have 62
that's a junior so if I look at my
number of trials right there
I had the four seniors I had two that I
threw away five six then I had Junior
junior that was eight trials right there
so it took me eight okay so I would have
eight or more up that's a trial for that
and then I'd have less than eight which
obviously didn't happen so then I can
either pick up like just go like this
and pick up right there or I can start
on a new line I'm gonna start on a new
line just because it's gonna be a little
less crowded here um you also have to
pay attention to repeated numbers I
wasn't super careful about that in the
last one because it's so small here but
I don't think I had anything repeats so
I'll show you one more trial 73 73 is a
junior PS if I were to say I got a 73 in
my last trial up here that's okay if I
get 73 in my new trial because it's like
a fresh start every trial is like a new
beginning right here so if I was gonna
write that out I would talk about a new
trial is like you start fresh so I have
a junior then I have a 67 67 is also a
junior so just like that I am full of
you I'm done with my juniors then I have
a 64 that's a reject 71 is reject 50 is
a senior 99 is a rejects 40 is a senior
uh zero zero is a senior this is really
hard to do with this tiny table here so
sorry if I'm making a mess of this I
don't know what I have right now I have
three senior 19 as a senior so I'd stop
right there then I count my trials one
two three four five six and that's at
least eight so that would be another
tally mark right here
my next time I do it in five trials I
put a tally over here etc now on a quiz
there aren't going to be very many
trials because it takes forever to do so
I'm gonna make you do like five trials
so say I did two trials right here I
would estimate the probability to be a
hundred percent because I only did two
out of two obviously that's not an
accurate probability but these problems
care a lot more about the fact that you
can actually understand and carry one of
these out rather than that you can get a
good accurate probability so just go
with the number of trials they tell you
to even if it's small your quiz will
have a problem something like this where
you guys set up a simulation and carry
out a small number of trials so that is
Click on any text or timestamp to jump to that moment in the video
Share:
Most transcripts ready in under 5 seconds
One-Click Copy125+ LanguagesSearch ContentJump to Timestamps
Paste YouTube URL
Enter any YouTube video link to get the full transcript
Transcript Extraction Form
Most transcripts ready in under 5 seconds
Get Our Chrome Extension
Get transcripts instantly without leaving YouTube. Install our Chrome extension for one-click access to any video's transcript directly on the watch page.
