Miscellaneous Examples : Part 1 Video Lecture | Mathematics for GRE Paper II

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the examples is the variance of 20
observation is 5 if each of the
observations multiplied by 5
find the new vegas so the question says
variance is nothing but Y numbers of the
business 20 and he's particular by P so
we know that the formula we have is
variance is equal to 1 by n Sigma X I PI
B Square where I is equal to 1 where
this problem in over here we know that
this guy is equal to 5 is equal to 1 by
n is equal to 20 into salvation of Exile
- mean square is equal to 1 2 nd this
thing cut or we can say that this time
same thing will particular body here d8
summation X I - routines 28 device
lifted here I can write I is this is my
first equation now if all the values of
x - oh something example X 1 X 2 16
values we have everything we multiply by
2 we get 2 X 1 2 X 3 right
makes me you'll call this Y then call
this as Y by 1 by 2 pi Z just for making
a license you should have 2 X 1 to make
sure who makes it as if I 1 y 2 y 3
where they say by I is equal to X this
is what they say correct oh you seen it
X is nothing but 1 by 2
that is my first official second ' now
you have to find the middle point we
know why will be nothing but by any see
how I cut there I is equal to what when
and why I say is I know 2x X so this
becomes 1 by n is nothing but 20 into
Sigma makes I okay I is equal to 1 2
since 2 is a cause-effect I can take
outside so this becomes 2 by 20 into
Sigma I said I is equal to 1 to thank
you
this is nothing but to wait to read
omics so we can say that we have I is
nothing but 2 a 2 mean of X right
because this whole thing is mean of Six
Sigma X I'm a Tony nominee to you this
formula we have X I is equal to PI a by
2 and we have mean of biased are due to
opening effects so here is popular now
this formula same from them to star it
so this complex so as their at Sigma X I
minus X mean square Y is equal to 1 to
20 this is nothing but something or I
can say X I is nothing but 1 by 2 by 1
by Y I - again XD is nothing but my mean
my do this equation by you mean by
square summation in I is equal to 1 to
20 is equal to perfectly I can take 1 by
2 comma here outside because one might
use a concept the becomes 1 by 2 square
into summation of I is equal to 120
why I - why mean square is equal to
hundred correct or I take this value
here and I'll take my to square here so
this becomes summation of why I - why
means I have is equal to hundred into
full because you square is 4 this is 400
and here I is equal to 1 to I is equal
to 1 to 20 so what we have seen if I
supposed to find a new variance because
I assume the new values by I the new
balance is the T word
you know where is nothing but 1 by n of
this so 1 by n is adequate and this is
21 by 20 of this this is 1 by 20 of this
this becomes T and that is so what we
have seen it was 5/5 became 20 so Phi it
became just well into this dream so
generally the theorem says that if there
is a variance and should multiply K with
all the number then the words every
suppose o be the new variance is nothing
but blue awareness becomes K square into
4 is no variance but suppose this is
Sigma square so the new variance is
nothing but K square Sigma square let me
write it once again here this is Sigma
square nu is equal to K square Sigma
square correct so if you multiply all
the number by K then the variance is K
square of the what we have done simple
nothing we must use the new variants to
be by I and we found that Y is going to
be
sigh and also be found them by means
vendor - it's me
let the end use this formula don't
follow me apart and sheet of X I can
explain you say bye-bye me and before
that this value turns out to thank you
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