Mean of a Random Variable - Probability, Class 12, Math Video Lecture | Mathematics (Maths) Class 12 - JEE

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now we have non random videos now we'll
learn the mean of random variables we
have some kind of believers will fight
before you mean abu zeid not believer
for example was I to enroll that we have
some family here which has and number of
families which has two three or four
members you want to select some family I
want to find the average of the number
of members in the family they also be
used mean right so and the mean is
denoted by mean so the values are the
values of X can be X 1 X 2 X 3 example
is a family the family member can be
equal right in toward let's suppose coin
twice the number of heads can be 0 1 or
2 night so those are the number of X 1 X
2 X variables the random variables and
the probabilities are broken random
variables are these we have found these
also right we have found each other in
two variables so the mean is nothing but
Sigma P I X I so till now if you see
what we have done is we have found X I
write P X I so we told that X can be 0 1
2 and for this let's suppose this guy
was and by 4 1 by 2 something like this
we have done so we know XIV top T I X I
now if you want to find the mean you do
that thing but you will be multiplied
these two moons
multiplied needs to multiply this to
that example this you get 0 this you get
2 and this you get 1 by 1 by 4 into 5
and that is what to me me is given by
new nothing but Sigma X I P we take some
examples to solve this we understand
this
so here a pair of die is thrown and the
random variable X that denotes some of
the number
that appears on the die surface so you
have two dice and you throw any fine to
solve the numbers and that is nothing
but the value of X find the mean of X so
the question is you throw this die honey
tie 200 times and you want to find what
is the mean or the some of them numbers
correctly so here you see the sum of the
numbers the minimum can be 1 plus 1/2
and the maximum can be right 6 plus 6 so
it can vary from first let's define the
sample space so it can be first guy can
be 1 second agreed upon first can give
one second you need to first once again
3 1 4 1 5 1 6 this is one set we start
with 2 2 1 2 3 4 5 - 0 second 7 3 1 3 3
3 3 3 4 3 5 3 6 this another set for 6
another same PI 1 5 2 5 3 5 5 5 5 6
under set 6-1 6-2 6-3 6-4 six five six
is the cursor but places we have been we
have some is going to do with this guy
for some is equal to 3 we if you see
this 2 will give 3 some for for you can
take these values right
simply over five you can take these
values so you really get for 6 you can
take these balance or 7 you can take
these values for 8 you can take these
values 6 plus 2 like this for nine you
can take some now you can take these
balance for 10 you can take these values
for leavening it takes
individuals types so if you see some is
equal to one you want to find parity of
X is equal to 2x with Miriam as to how
many keys you're getting one total how
many possible combinations 6 into 6 36
if you see here so no parenting of x-men
2 1 is 2 is 36 similarly probability of
X would be 3 so much 2 numbers for each
semester 36 2 remarkably the sum is 3 to
do whether this is where it if or X is
equal to 4 there is soft numbers but
before there are three numbers so it is
3 matrices plenty of X identify they are
you see even find there are four numbers
I'd want to keep this whole life now
we're adding of sum is 6 is nothing but
there are five numbers whose sum is 6 no
parity of X equal to 7
there you see 6 numbers for which some
itself X is equal to 8 for 8 if you see
1 2 3 4 5
there 5 number for which some is a 24 X
equal to 9 1 2 3 4
there are four numbers for which sum is
nine
similarly for coverity X is equal to 10
they are one two three numbers for 11s
some we are to number six five and five
six two numbers for well as some is only
one number successes this is my property
distribution so I am told that mu is
nothing but Sigma X I PA where I is
equal to two
correct we'll put a Lada is going to do
into p2 you do the word 1 by 36 is equal
to 3 T 3 is 1 2 by 36 to us i is equal
to 4 B 4 3 by 36 is equal to Phi D Phi 4
by 36 I is equal to 6 p 6 PI within 6 is
equal to 7 p 7 6 because it is equal to
8 p.m. by becomes X Phi is equal to 9 p
9 5 because it is equal to this Korea 9
p9 is omegas is good 10 3 by the CC is
equal to 11 11 2006 Phi is equal to 12
and PIPA the 6yz p11 is one method we
should hide all these what you get is
not that difficult but yeah I understand
a little let me hear you have to find
all the variables known values of x that
is to well where these of all the values
of x and then we have to multiply now
let's take one simple example here we
find the mean number of heads in three
toss of a coin so I have one coin and I
tossed it twice right so if you see the
distribution can be you can get head or
tail first time then you may get a hint
of T head or teen who made the head tail
head tail again head tail distribution
will get something like head head head
head head tail
so if you see these possible that is
impossible so I'm looking for the number
of heads so my X is nothing but number
of heads so you can have a zero value
Luallen you value 1 2 1 1 and so this is
3 yeah 3 hits a right so it can have X
can have values from X and have values
from 0 1 2 and so let's find priority of
X equal 0 this number of head is pillows
it is nothing but the variety of head
head head you see this is another 1 by 8
because there are 8 possible options and
this is 120 of X is equal to 1 you see
there are three positions we have these
things this becomes 3 y where if you
have X's you can also you see there are
three positions where you get X is going
to do he by parity of X is equal to 3
you see the only one position you get X
is 1 2 3 so you see the mean is nothing
but Sigma P ixi right and X is nothing
but I is nothing but from 0 don't you so
X 0 is what 0 0 into 1 by plus 1 4 1 it
is 3 by 2 for 2 T 3 by last 3 for 3 days
gone right now what you get is 3 by 3 so
the mean number of head for the 3 terms
of minus 3 by 2 correct simple one we
have to find the vanity and first you to
find the random variable random variable
here is number of heads and that can
vary from 0 1 2 or 3
you find the repair of the distribution
for these and you find them two dice are
thrown some additional the external
number of sixes find the mean of
expectation nothing but mean of X so the
number of success can be one six two six
or both can get six right so provided
says
the independent thing so for vanity of
getting six is what 1 by 6 and duality
of not getting this is what fibrous is
right because all independently so 4x is
equal to 0 that means there is no six
I'm looking for six times six times that
anyone priority of six - into a value of
6 - 5 by 6 into 5 versus 4 X is equal to
1 you may get 6 in the first row or you
may get 6 in the second row right this
is nothing but 6 in the first row is 1
by 6 into 6 - 5 by 6 plus 6 staff it is
5 by 6 into 6 small message right so
what you get is 10 by thermoses
similarly in both the throw you want 6
I'm looking for the value of 6 6 that is
a variety of 6 into primality of sixes
that is nothing but 1 by 6 into 1 by 6
the melody of sixes on my six and what
you get is 1 by 2 this is you want to
find you nothing but X ipx8 is wrong 0 -
well so I 0 4 0 it is 25 by 36 maybe 5
by 36 + 1 for the one it is 10 by 36 for
to blue it is 1 by Genesis we saw all
this you get 1 by 3 so you see that the
mean number of sixes is 1 by 3 okay
thank you
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