a very warm welcome to this course on probability
foundations for electrical engineers now ah
many of you might have probably heard of probability
might have already learnt probability before
ah and i am sure you agree that probability
is used for modeling so many things in life
ok all around us you see so many things are
random and its good to know probability ah
but this course is specifically targeted at
electrical engineers and you might wonder
why in electrical engineering probability
is important
now i would like to give you a few examples
in the area of electrical engineering where
probability plays a very important role ah
the first ah case is when you want to model
noise in systems now many ah circuitry and
circuit elements have noise in them if you
want to communicate information from one point
to another you have to face noise
now noise is a complicated phenomenon occurring
because of various physical factors now its
not possible to write down exact equations
for all those physical factors and we give
up and model it in a probabilistic manner
and that probabilistic model has been extremely
successful you see circuits all around you
you know integrated chips and all that that
are functioning ah in spite of noise in a
very wonderful manner and thats because we
really understand how noise works and you
see so many communication systems around us
communicating in the presence of noise without
any errors and thats once again because we
understand the probabilistic noise model very
very well
noise is not the only thing that is modeled
using probability in electrical engineering
one more important area is ah lets say communications
networking ok or even signal processing ok
quite often ah phenomenon in a computer network
is probabilistic so if you imagine a cellphone
network ok not just necessarily a computer
network any communications network for that
matter a cellular phone network if you want
to say deploy a cellular phone network you
have a certain fixed bandwidth and you want
to serve as many mobile phones as possible
and while so many people have mobile phones
not everybody is talking at the same time
once in a while you pick up the phone turn
it on and want to talk and even when you are
talking ah you you may you may not you may
not be talking continuously for a long time
you may be talk for one minute maybe talk
for three minutes maybe talk for two minutes
etcetera etcetera
so now you have a situation where you have
so many users whom you want to connect in
a communication network and you dont know
who is going to be on at what time how long
are they going to turn on how do you connect
how do you give give them resources like bandwidth
and time etcetera all of that is also random
and when you deploy communications networks
like that you have to have a very good understanding
of the randomness in that phenomenon and be
able to model it probabilistically and use
it in your system deployment otherwise you
will be wasting a lot of bandwidth bandwidth
as you know is very very expensive
now similar situations arise in signal processing
so today ah speech recognition is considered
a very important problem and speech the speech
signal is essentially random when you want
to build a speech recognition system you have
to imagine that the speech signal coming at
you is random in some sense and you have to
be you have to model it probabilistically
and you have to build devices which can understand
that model and use that model and ultimately
recognize what is being spoken etcetera etcetera
so hopefully i have convinced you that there
are enough applications in the area of electrical
engineering for probabilistic models and probabilistic
models play a vital role today in so many
aspects of systems that we see everywhere
ok ah now a few words about this course in
particular this course is titled probability
foundations so we are not going to be doing
so much applied probability while i gave you
some examples of systems we will never talk
about systems in this course its more about
the basics of probability built from the ground
up from basic axioms basic definitions we
will use very simple experiments like tossing
a coin throwing a die picking a ah card from
a pack of cards throwing balls into bins things
like that very simple experiments to clearly
bring out the fundamental foundational concepts
that are needed for understanding larger system
ok so this is a introductory course a first
course in probability and the idea is to teach
you the foundations so that you can take more
advanced courses going forward in the future
ok
now what kind of prerequisites do you need
you will need basic calculus a good foundation
in basic calculus you should know the real
number system you should know the number system
you should know what are functions you should
know ah things like continuity differentiation
integration particularly multivariable integration
even two variable integration is ah very very
useful in this course all these things we
will assume you know ah one particular function
that will play a very important role is the
exponential function and you should know a
little bit about that and its counterpart
the logarithm function also something that
you should know very well
and other areas of mathematics ah its good
to have a general competence in mathematics
ah for instance set theory you should be comfortable
with and and basic you know summing of sequences
all of those things you should know ok ah
thats about prerequisites and the course is
structured in a in an easy manner we are we
are we are introducing the concepts over eight
weeks there will be enough examples there
will be ah a lot of problems assignments are
extremely important in probability you really
learn probability only by solving problems
i hope you have a enjoyable time in the rest
of the eight weeks of the course and together
with professor aravind who is one of the main
lecturers in the course ah my name is andrew
thangaraj both of us will be handling this
course for you i hope you have a wonderful
time
thank you very much
