This video tutorial explains how to calculate the expected value (or mean) of a discrete probability distribution using a clear formula and practical examples.
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hello class
welcome back to our channel in this video
video
i will show you how to solve the
expected value
or the mean of a discrete probability distribution
distribution
so on 4 millimeter nut and guys is
e of x which means the expected value
is equal to the summation of x
times f of x where x
is the element of the support
okay so let's have example number one
so let x be a discrete random variable
and s is equal to 0
1 2 3 be
its support so the probability must function
okay so as you notice in your acting
probability though is one for it
if x is element of s
which means your x naught n is zero
one two three okay
then the probability is zero if
otherwise okay or if x is not an
element of s so parabola solves nothing c
c
expected value nothing
submission x or x times f of
x so i've been adding summation guys
being a sum of all or even
or plus nothing x
times f of x okay
which is zero
so we have zero times
f of x so on f of x not n is one fourth
plus next nothing s is your one
plus two times
f of x which is one fourth
plus three you're adding last nine
x times one fourth
okay so simplifying nothing you know nothing
nothing
formula so zero times one fourth the
zero or cancel out plus one times one
fourth we have one
fourth plus two times one fourth this is
two over four
so the pokemon multiply line and whole
number to fraction
multiply like nothing you adding whole
number during the numerator
okay then copy the denominator
then three times one fourth this is three
three
over four okay
so simplify nothing so since
denominator so copy language in denominator
denominator
then 1 plus 2 plus 3
is equal to 6 or
this is 3 over 2
so in decimal number and this is 1.5
now however guys so let's have another example
example
number two so let x be a discrete random
variable with support as
one two three
where f of x is is equal to
1 over 6 times x if
x is an element of s so if it's a b
n 1 2 3 x
in volume adding a random variable
probability is one over six times
x okay then zero number
if otherwise okay then we asked to
compute for d
expected value no adding x
so again so using the same formula we have
have
the summation of x times f of
x okay
so it's a given at n and first value now
x naught and is one
times f of x which is one over six
x so on my action adding a probability
so unfortunate x nagina with nothing is one
one
okay so meaning multiply nothing see one
over six
by one
okay plus your next
value number x naught n which is two
times f of x which is one over six
x so on x nagina with nothing theta is two
okay plus three
times f of x which is one over six
okay now however guys so simplify nothing
nothing
so one times one over six times
plus two times one over
six this is two over six then times two
we have four over six
okay so again multiply time whole number
to fraction
numerator long time multiply then three times
times
one over six that is three over six
then times three that is
nine over six okay
so since uh we have common denominators
so bring down
nothingn then we have 1 plus 4
plus 9 which is 14.
so therefore the expected value
is equal to 7 over 3
okay so next let's have example number three
three
so find the expected value of
x so this time we have a discrete
probability distribution so we have six
random variables which is one
two three four five and six then your
probability in a minor adding a
random variable is we have point fifteen
random instead of using
uh x times f of x this time we have x
times p of x okay
x times p of x okay so you move to play
like that and see x
the answer i think corresponding p of
x so 1 times point 15
so we have uh 0.15
then 2 times 0.25 this is 0.50
3 times point thirty so this is point
ninety then four times fifty point fifteen
fifteen
we have zero point sixty then
five times point ten this is zero point
fifty then six times
point zero five we have zero point
thirty okay so after in yamagawa guys
you are adding
50 plus 0.90 plus
0.60 plus point fifty
plus point thirty we have the
two point ninety five
okay so it on two point ninety five eta
magicking expected
value all right
joba guys so this is the end of our video
video
i hope mina to tune in so if you have
questions or clarifications kindly put
them in the comment section
below so thank you guys for watching
this is prof d
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