This content explains the concept of random variables, which are numerical outcomes of random experiments, and differentiates between discrete and continuous random variables with examples.
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hello class
so in this video our topic is all about
exploring random variables
so a random variable is a function that associates
associates
a real number with each element in the sample
sample
space so when we say a sample space
of a random experiment
so it is a variable whose values are
determined by chance
does in a simple words a random variable
is a numerical quantity
that is derived from the outcomes of a random
random
experiment so let's have an example of a
random variables
so for letter a in the experiment of
tossing a coin the number of times
that the coin turns up ahead is an
example of
a random variable so
example is a number of times now
coin as head then credit
okay then for letter b suppose
two dice are rolled the sum of the two
numbers that face
up is an example of a random variable
so i'm adding random variable data is
young sum
experiment okay so let us see
suppose this spinner shown below is spun
so we have four numbers satin spinner one
one
two three four so
nothing um random variable
such as networks experimental is the
number of times that the spinner stops
i think at number three
okay so pedrina number one number two
or number four
okay so next is let's have these steps
on how to find the value of the
random variables on any events or
experiments so this time guys
nothing you value nothing random variables
variables
so in step 19 is we need to assign letters
letters
that will represent each outcome
number two determine the sample space
experiment the number three is we will
count the number
of the random variable
so let's have example number one
uh suppose three coins are tossed
then let x be the random variable
representing the number of heads
so dito adding random variables the
number of heads that will occur
so find the values of the random variable
variable
x okay so first
um letter is a
so let's say uh let h
represents the head then
outcome okay next is for
coin 2 then after nothing
we have head tail
head then from our path we have head
five we have tail head
head then six nothing we have
tail head tail
starting eight and nine uh seven eighth
number we have
tail tail head and tail
tail tail okay
so after nothing malicious down our all
possible outcomes
within another name guys you values now
adding random variable x
i'm adding variable x is you number of heads
okay so
so i think first outcome a number of
head snap and i3
the second outcome we have two then
support lobby of two
then one the number of heads we have two
then one then one
then starting last outcome is
zero okay so as you can see
i know uh four values don't add in
random variables which is young zero
one two and 3
okay so the possible values
of random variable x are 0
1 2 and 3 and we can also say that
x is equal to zero one
two three okay
so number guys combine up in uh in an
optimal possible values nothing
random variable x so next let's have
example number two so
suppose there are two people
to be tested in coffee 19
so let x be the random variable representing
representing
the number of infected person that occurred
occurred
so find the values of the random variable
variable
negative 19.
negative okay so can be belonging
event not then we have four uh possible
outcome we have one two
put the minimum negative positive then
negative negatives okay
then after nothing is done like possible
outcomes nothing
is your number of infected
is positive saturated outcome we have
uh one positive then density last
possible outcome
i zero young positive
are you infected okay so
the values of the random variable nathan
is zero
okay so next let's have the two types of
random variables so the first type of
random variables is young discrete
random variable so this variable can
only take a finite
number of distinct values so the values
are exact
and can be represented by non-negative
whole numbers so meaning it's a discrete uh
uh
discrete random variable nothing young
values nothing detail was not obtained
by using counting
okay or bini b lam while in a continuous variable
variable
it can assume an infinite number of values
values
in an interval between two specific values
values
so they can assume values that can be
represented not
not only by non-negative whole numbers
but also fractions and decimals
and are often results of measurement
so the main difference non-continuous
variable discrete
is the continuous variables management
of fractions or
values is not obtained through uh measuring
measuring
now while it's a discrete is by counting tithing
tithing
or poor whole number islam okay
so next uh let's have an example
so classify the following random variables
variables
if discrete or continuous
so for letter a number of patients per day
day
at hospital nang muntin lupa sodito
i'm nothing variable is your number of patients
patients
so para mahuva nathan guys young number
of patients nothing
is belonging or by counting
okay so it means now this variable is an example
example
of a discrete variable
okay next for letter b we have temperature
temperature
of the copied 19 patients
so since um is temperature and alumni
continuous okay
for letter c the number of male
athletes so again uh
poor whole number long time or maybe
long since
is the number of male athletes so it means
means
this is a discrete variable
in a cup of coffee through measuring
okay so it means this is a continuous
okay then last one letter e
is the number of deaths infected by
covet 19
in muntinlupa so since you number of
that's nothing is bini biran
and at the same time is um values nothing
nothing
is finite numbers or or non-negative
whole numbers
so this is a this discrete variable
okay so this is the end of our video i
hope main attorney and kaios so if you have
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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