Mean and Standard Deviation of Binomial Distribution, Business Mathematics and Statistics Video Lecture | Business Mathematics and Statistics - B Com

okay mean variance and standard
deviation of a binomial distribution so
there's your three formulas obviously
this first one that's mu which
represents mean
so there's your mean here's your
variance formula and here is your
standard deviation formula to kind of
interpret what you need out of this
obviously mu stands for mean this symbol
right here Sigma squared stands for
variance and Sigma is just the square
root of Sigma squared is stands for
standard deviation and what we need to
determine then next is what does n mean
what does P mean and what does Q mean KN
is the number of trials like for
instance if I was flipping a coin ten
times I would be n would be ten if I was
going to predict the weather over the
next five days where the probability is
the same each day that would be so ten
days n would be ten so it's just how
many are in your sample or in your not
in your sample but in your population
what you're what you're doing P stands
for the probability of a success and Q
stands for the probability of a failure
you know maybe a successes heads and a
failures tails so probability of a head
would be P Q be the probability of a
tail and if it's a fair coin they're
both 1/2 so let's look at an example of
this so let's say let's say we have a
20% chance of rain over the next 5 days
you know each day there's 28 a 20%
chance of rain so it's the same each day
so n would be 5
P would be 0.2 and Q the no rain would
be 0.8 and so your mean would be 5 times
0.2 which is 1 standard deviation Sigma
squared is 5 times 0.2 times 0.8 which
that would be I could probably I be I'll
just do it so I don't screw it up so 5
times 0.2 times 0.8 is 0.8 yeah do that
but anyway and then your standard and
your yeah your standard deviation will
be the square root of that so the square
root of 0.8 which that's a little
trickier it'd be point eight nine for
approximately and you always go one
decimal beyond our data so our data is
to the tenths place so really it's just
point eight nine okay
and so that is your how you find mean
standard deviation and variance of a
binomial distribution curve simple I
think so good luck and see you next time