0:10 hello class
0:13 so in this video our topic is all about
0:17 exploring random variables
0:20 so a random variable is a function that associates
0:20 associates
0:23 a real number with each element in the sample
0:24 sample
0:27 space so when we say a sample space
0:38 of a random experiment
0:40 so it is a variable whose values are
0:43 determined by chance
0:46 does in a simple words a random variable
0:49 is a numerical quantity
0:52 that is derived from the outcomes of a random
0:53 random
0:56 experiment so let's have an example of a
0:58 random variables
1:01 so for letter a in the experiment of
1:04 tossing a coin the number of times
1:08 that the coin turns up ahead is an
1:08 example of
1:13 a random variable so
1:16 example is a number of times now
1:19 coin as head then credit
1:27 okay then for letter b suppose
1:30 two dice are rolled the sum of the two
1:31 numbers that face
1:35 up is an example of a random variable
1:37 so i'm adding random variable data is
1:38 young sum
1:59 experiment okay so let us see
2:03 suppose this spinner shown below is spun
2:06 so we have four numbers satin spinner one
2:06 one
2:10 two three four so
2:13 nothing um random variable
2:17 such as networks experimental is the
2:21 number of times that the spinner stops
2:24 i think at number three
2:28 okay so pedrina number one number two
2:32 or number four
2:35 okay so next is let's have these steps
2:39 on how to find the value of the
2:42 random variables on any events or
2:46 experiments so this time guys
2:48 nothing you value nothing random variables
2:49 variables
2:52 so in step 19 is we need to assign letters
2:54 letters
2:57 that will represent each outcome
3:01 number two determine the sample space
3:09 experiment the number three is we will
3:10 count the number
3:13 of the random variable
3:17 so let's have example number one
3:21 uh suppose three coins are tossed
3:24 then let x be the random variable
3:27 representing the number of heads
3:30 so dito adding random variables the
3:32 number of heads that will occur
3:36 so find the values of the random variable
3:37 variable
3:40 x okay so first
3:44 um letter is a
3:52 so let's say uh let h
3:55 represents the head then
4:33 outcome okay next is for
4:36 coin 2 then after nothing
6:53 we have head tail
6:57 head then from our path we have head
7:05 five we have tail head
7:08 head then six nothing we have
7:12 tail head tail
7:15 starting eight and nine uh seven eighth
7:17 number we have
7:20 tail tail head and tail
7:24 tail tail okay
7:27 so after nothing malicious down our all
7:29 possible outcomes
7:33 within another name guys you values now
7:36 adding random variable x
7:40 i'm adding variable x is you number of heads
7:46 okay so
7:49 so i think first outcome a number of
7:52 head snap and i3
7:54 the second outcome we have two then
7:57 support lobby of two
8:02 then one the number of heads we have two
8:05 then one then one
8:09 then starting last outcome is
8:14 zero okay so as you can see
8:18 i know uh four values don't add in
8:22 random variables which is young zero
8:26 one two and 3
8:30 okay so the possible values
8:34 of random variable x are 0
8:38 1 2 and 3 and we can also say that
8:41 x is equal to zero one
8:45 two three okay
8:48 so number guys combine up in uh in an
8:51 optimal possible values nothing
8:55 random variable x so next let's have
8:58 example number two so
9:02 suppose there are two people
9:05 to be tested in coffee 19
9:08 so let x be the random variable representing
9:09 representing
9:12 the number of infected person that occurred
9:13 occurred
9:15 so find the values of the random variable
9:16 variable
9:38 negative 19.
10:35 negative okay so can be belonging
10:39 event not then we have four uh possible
10:41 outcome we have one two
11:02 put the minimum negative positive then
11:07 negative negatives okay
11:11 then after nothing is done like possible
11:12 outcomes nothing
11:22 is your number of infected
11:44 is positive saturated outcome we have
11:47 uh one positive then density last
11:48 possible outcome
11:52 i zero young positive
11:57 are you infected okay so
12:00 the values of the random variable nathan
12:01 is zero
12:08 okay so next let's have the two types of
12:11 random variables so the first type of
12:14 random variables is young discrete
12:18 random variable so this variable can
12:19 only take a finite
12:23 number of distinct values so the values
12:25 are exact
12:29 and can be represented by non-negative
12:32 whole numbers so meaning it's a discrete uh
12:32 uh
12:35 discrete random variable nothing young
12:38 values nothing detail was not obtained
12:40 by using counting
12:43 okay or bini b lam while in a continuous variable
12:45 variable
12:47 it can assume an infinite number of values
12:49 values
12:51 in an interval between two specific values
12:52 values
12:55 so they can assume values that can be
12:57 represented not
13:00 not only by non-negative whole numbers
13:04 but also fractions and decimals
13:08 and are often results of measurement
13:10 so the main difference non-continuous
13:11 variable discrete
13:15 is the continuous variables management
13:16 of fractions or
13:24 values is not obtained through uh measuring
13:25 measuring
13:28 now while it's a discrete is by counting tithing
13:28 tithing
13:32 or poor whole number islam okay
13:36 so next uh let's have an example
13:39 so classify the following random variables
13:39 variables
13:43 if discrete or continuous
13:46 so for letter a number of patients per day
13:47 day
13:51 at hospital nang muntin lupa sodito
13:53 i'm nothing variable is your number of patients
13:55 patients
13:57 so para mahuva nathan guys young number
13:59 of patients nothing
14:03 is belonging or by counting
14:06 okay so it means now this variable is an example
14:07 example
14:12 of a discrete variable
14:15 okay next for letter b we have temperature
14:17 temperature
14:20 of the copied 19 patients
14:26 so since um is temperature and alumni
14:47 continuous okay
14:50 for letter c the number of male
14:53 athletes so again uh
14:56 poor whole number long time or maybe
14:58 long since
15:01 is the number of male athletes so it means
15:02 means
15:05 this is a discrete variable
15:17 in a cup of coffee through measuring
15:20 okay so it means this is a continuous
15:26 okay then last one letter e
15:30 is the number of deaths infected by
15:32 covet 19
15:35 in muntinlupa so since you number of
15:37 that's nothing is bini biran
15:44 and at the same time is um values nothing
15:44 nothing
15:48 is finite numbers or or non-negative
15:49 whole numbers
15:56 so this is a this discrete variable
15:59 okay so this is the end of our video i
16:01 hope main attorney and kaios so if you have
16:01 have
16:04 questions or clarifications kindly put
16:06 them in the comment section below
16:08 so thank you guys for watching this is
16:09 prof d
