Examples : Probability Distribution of a Random Variable Video Lecture | Mathematics (Maths) Class 12 - JEE

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let's find the probability distribution
for the number of doublets in a
free-throw for a pair of tights so we
have this die and we throw it three
times this particular eye is thrown
three times and doublet wins what
doublet if you see then the same number
that is giving it one 1 two 2 three 3
four 4 five 5 six this is the doublet we
defined the probability distribution of
number of doublets so in one throw in
one throw the verity of doublet is what
this means 6 by 6 numbers by total ill
mentally 6 into 6 6 by 36 that is wrong
vs. similarly probability of not doublet
will be 1 minus 1 by 6 correct the best
so I have the polarity of goblet and I
have the wear idiom not done it correct
since I am throwing it twice thrice it
may happen that I gave make a doublet in
zero times none of the clothes I make it
a bit in one times two times and three
times right I make it up it in one times
two times and three names so let's all
this for one times the way we're done it
is pro Verity of X is equal to zero it
is random variable X is equal to 0 is
nothing but you get don't them you do
either your own interpreter as you are
looking for no parity of mm - double it
the interpreter you don't get the ready
any throw right since they are
independent events this is nothing but
ability or D dash into fidelity of
LD off D - and that is nothing but 5 by
6 into 5 by 6 PI by 6 and there is
nothing but 125 bite that does mine X is
equal to 0 that is this 0 W the second
is 1 doublet so what David can be the
first guy can be developed second - guy
may not be doubling the second guy can
be doublet in this case the third guy
can be doubles q option for one dove it
they are also independent events I can
write this as nothing but probability of
D - D - G - D - like that so if you saw
this this becomes weary of D is what 1
by 6 D - is 5 by 6 into 5 s 6 + D - is 5
by 6 DS 1 by 6 in 3 - 5 by 6 plus D - is
5 by 6 5 essence and DS the rest's
correct so if you solve this you get 50
75 by works that is probability X is
Bourbon ma where any X is going to - so
I'll take this part not so it can be via
you are to dub dub its so it can be
first to double its it can be first and
last W or it can be last to the right
three options so you solve this guy also
doublet is 1 by 6 again doublet 1 by 6
not double it is 5 by 6 plus again
doublet is 1 by 6 not doublet is 5 by 6
or getting doublet is Mumbai 6 plus not
doublet is 5 by 6 doublet doublet 1
lessons we solve this what you get is 15
by once
similarly severity for getting 3 double
its is nothing but well if your doublet
doublet doublet and that is nothing but
1 by 6
to invest in civilian vessels correct
element 1 by 2 so the provided a
distribution if you see will be you have
the balance of X 0 1 2 & 3 and here you
have the probability of X for 0 it was
125 by 2 1 6 4 1 it was 75 by 2 160 or
do it was 15 by 2 1 6 4 3 it is 1 byte
and if you add if you see if you add P P
I where I is equal to 0 to 3 what you
get is 125 plus 25 is 200 plus 15 to 15
plus 1 to 1 6 by 2 and 6000 you this is
the probability distribution of random
will use these things to find me sign
and division all the future flights but
just now understand that random
variables are nothing but very well
whose values if another pandemics plane
and we can find the probability
distribution of a random so the question
says on contains 5 red to greens balls
two balls are drawn randomly X represent
the number of green balls what are the
possible values of x and is excellent
available so you have one which has two
greens and five red balls two balls are
drawn so if two balls are drawn zero can
be green one can be green or you can be
right both can mean three possible
scenarios correct so through parity of X
is equal to zero that means zero green
is nothing but the value of getting rid
of red correct so since it is without
replacement without obviously right so
maybe red one red two enhancing Salma
get G 1 G 2 I mean any any to determine
who the different actually
so this is nothing but 2 different red
numbers right first is a second is red
so this is nothing but probability of
red 1 into probability of red 2 given
first is red
please note it is not independent not
independent why because we are not
replacing it we are not we are taking
out the ball first bought they are not
replacing it so this will be the value
so this will become provide Li of red
one will be 1 2 3 4 5 total is 5 red and
to clean total 1/7 so first red provided
he will be 5 by 7 the second case so by
limiting of again red given the first
one instead will be in this case you
took out one red so you are left with
for rent googley total 6 and read your
left is for this will be the temerity of
second red given first right correct it
will come out to be 21 for you please
note it is not an independent variable
right so here 20 of r1 r2 identify -
prevent you are wearing to r2 I write
who this guys are - given R 1 is of
independent variable this preventive are
to given alpha is nothing but 24 do tell
so in this we can fight so this is where
you get the validity of X equal to 1/1
red right sorry 1 green so it can be
have red green or green red so this is
nothing but Coverity of read into
probability of green given first instead
last ability of green into probability
of red even first is green so remain
ready of red is we know nothing but 5 by
7
where do you have green even first is
dead so if first is red you are left
with 4 red you greens so frivolity of
green here will be 2 by 6 because 6
balls or the wish to agree
Plus where do you agree in the first
instance will be two greens out of seven
balls 2 by 7
provided your bread even the first one
says green was you are left with 1 green
and 5 end right this condition you
should take one green out of this so you
are to find the probability of
that is five read out of six was correct
so if you add this you get twenty why
the parity of X is equal to one that is
probability of both green there is
nothing but ability of green one into
Pro value of green to even first
fernsley so providing a griever is
nothing but they are two greens out of
seven balls start with you took out one
green you are left with one green six
and five red there is one green end
total five plus one six spots there is
nothing work you buy for it so we see
all the values are less than one and if
you add these values 20 by 40 to 20 by
40 20 by 40 to you get one if you add is
20 by 40 to plus 20 by 40 plus 2pi upon
it you get what do you buy body do that
is since the sum is coming out everyone
and now garlis one you can see that yes
it is a random there is the trick here
was that it is not a independent event
so you have to take care so the question
says when express will may be the number
of heads and number of things
often when a coin is tossed six times
was the value of XP asking for so six
times it can have six head 0 team right
5 head one time for head
putain three head three pane to head for
tail one head 5 t + 0 head 16 let's find
the difference so in this case
difference will be 6-0 6 in this case
this will be 5 minus 1 is 4 different
middle number of head and tail here 4
minus 2 is 2 3 minus 3 is 0 again 2
minus 4 is minus 2 but will take the
positive part because in this asked to
find difference between head and tail so
here until difference here it is again 2
here 1 minus 5 is minus 4 returning
positive part or
your minus X is minus 6 and I'll take
the positive part 6 so if you see the
difference are only 0 2 4 6 so the value
of x can be 0 to 4 so these the
conceptual question vehicle this time or
the most values of X so that you can
solve similar kind of questions where
you define now let's suppose find a
random variable the priority of random
variables all other random provided a
distribution for this case so again you
know the value of x can be these values
and again find them
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