Variance, Standard Deviation of Random Variables (Part - 28) - Probability, Maths, Class 12 Video Lecture

hello friends this video on to
Valledupar 28 is brought to you by
example your car no Murphy from exam
before watching the video please make
sure that you have watched part 1 -
foundry 7 since we know that me is not a
clear picture if you have some data
various gives a clearer picture on the
data you may have some differential of
data which gives the same being but the
data is different and you may not be
able to actually find the difference
right so if you want to know more on
these you can watch my previous videos
in class 11 or mean-variance where we
explain with a cricket example score
example why variance is a better option
than me and those we lost 30 variance
I will not discuss why variance is
better options and mean in this chart
because we already covered that graph to
level you can watch the video so there
are certain scenarios where mean is not
a better option they are they may be to
celebrate our she gives the same mean
but they are actually different right so
in that case a variance gives a better
picture so we study various odds when
you're studying this in class 11 now
we're studying the variance for the
random variable so if my mu is the mean
mu is the mean the variance of X is
divided by our X or Sigma X square and
that's value is X I minus mu square nu P
X nice it is only one X I minus mu mu
square into DX I square correct the same
formula for variance we are just using
it for preventing random variables it is
also e of X minus mu square C mean is
e^x you see and this guy is root oh ye
oh this guy X minus me
if you are confused with this formula
it's ok bu anyway a lot use this formula
again use another form which will derive
you solve the problems then similar to
the variance formula if you have issues
more issues and variance chapter again
watch the previous videos videos
standard deviation is nothing but root
of variance so the variance here was X I
minus mu square in pxi summation so the
root of the system division since the
formula is complex will derive another
formula for standard deviation standard
deviation is nothing but e x square
minus e of X whole square then X square
is nothing but X square i PX I this
formula is very handy actually so I will
explain how we got this formula we know
what till now that variance of X is
nothing but summation of X I minus this
mean square into px will expand this X I
square plus nu square minus 2 X mu into
px n correct so this become summation of
X I square DX I plus nu square PX i
summation minus 2 into summation now or
2 mu into X i PX m correct this is
nothing bad if you see right it is
nothing but e X square Y because your
dxi Square and you multiplying with P is
in final summation plus mu square PX i
summation P X I is nothing but 1 if you
see write summation P X I is 1 below
that this guy is 1 right so there's
nothing but this guy is nothing but u
square into summation of P X I this guy
is 1 we know that - 2 beam
summation of this guy is nothing but we
only using X IPX I Sigma this guy's you
so what I'm getting here is this is
nothing but e X square plus this becomes
mu square minus 2 nu star so what I am
getting is e X square minus mu square
and that is a simple formula we have and
we'll use this fall that will get
answers let's take one example find the
variance of the number obtain the throw
of an unbiased die so we have this die
and you throw it you may get one two
three four five six right so X will be 1
2 3 4 5 6 because the very is the way
you're looking for the number obtained
so number one can be one two three four
five six now we know that so where do
you of X is going to 1 is 1 by 6 all its
going to one methods actually the value
of x2 will also be equal to over D or X
equal to 3 is also equal to 20 of
expanded fold is equal to infinity of X
going to 5 is it going to do proved
already of X is equal to 6 all our one
message correct now I define variance
variance is nothing but e of X square
minus y X whole square right so let's
find G of X square there is nothing but
Sigma X I Square t X I I is 31 to 60 so
this becomes 1 square into P of 1 by I
is P of x squared over is 1 by 6 plus 2
square P of x squared plus 1 by 6 plus 3
square P of X equal to 1 by 3 1 by 6 was
for square P of X equal to 4 is also on
my 6 plus 5 square P of X go to for 6
square y of x per degree correct and
this comes out to be 91 license let's
find the mu here
new hair is Sigma X I X I I is equal to
1 to 6 that is something like 1 into P
of X plus 2 into P of X plus 3 into P of
X plus 4 into P of X plus 5 into P of X
plus 6 e TP is correct so this is
nothing but 2106 so my variance is e of
X while this 91 by 6 minus V of X that
is 21 minus X whole square right G of X
square this comes out to be 91 by 6
minus 4 41 by 36 this is 35 5 and that
is my test correct so not that difficult
I had this this random distribution so
the formula was a of X square minus P of
X whole square I found a of X square I
found a V of X you got them so the
quotient says two cards are drawn the
doubter placement please notice without
replacement
well stuff pack of 52 cards find the
mean variance and Sunday which means
number of King so mayor X here is number
of kings
so I have my discard number of Kings if
you see is there for Kings
it in a card there workings for games so
if two cards are drawn either none of
the working one can be king all mode can
be king right so where in T of X is
equal to 0 is none of them is King is
nothing bad from none of them Cape is
king that means I am talking about
zero king that means the card that I
have drawn is out of 48 cards because
they are 48 not King and cookie right so
that means I am taking a card to card
from 48th card and the reminding will be
divided by BBC correct you take two card
out of this going to God the preventing
that down them is king is 48 CP by T 0
when one is king is from 48 you take out
one card and from four you take out one
card right divided by introducing you
only that both our King is wrong for you
take out two guards by reduce it correct
the thyroid is you have done this thing
in the previous classes how to find the
trebling systematically so none of them
is a king you take two cars from 48 card
one of them is king you take one card
from 48th card and four card from one
card from four card one card from King
one card from honking you cut from non
game here both cards from King right so
this guy comes out to be 180 by two to
one this guy comes out to be 32 by 51
and this guy comes out to be 1 by 2
correct this is my probability
distribution now I do find mean variance
and standard deviation so mean if you
see he is nothing but Sigma XII FX I so
Sigma X I T X n so x value 0 0 into P X
I is 185 to 2 1 plus X go to 1 into 32
by 2 to 1 plus X guru into 1 by 2 to 1
if you solve this you get 3 4 5 now I
have to find variance covariance my e x
square is required to let's find this
guy also the resulting word Sigma X I
square P X I that is 0 square into
188 by QP 1 plus 1 square into 30 by 2 1
plus mu square nu 1 right and that comes
out to be 36 by 2 correct
so my variance if you see something bad
Y of X square minus e X square that is
nothing but 36 by 2 1 minus 34 by 2 1
square we saw this is nothing but 6 a
double 0 by 2 P 1 square and if you see
standard deviation this this guy is
nothing but root or variance there is
nothing but mu r o6 h 0 0 by p 1 square
and there is nothing but root 6 8 0 0 by
2 1 we saw this comes out to be point
user so I got all this not very
difficult easy to find
let's see thank you
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