0:10 hello class
0:13 welcome back to our channel in this video
0:13 video
0:16 i will show you how to solve the
0:17 expected value
0:20 or the mean of a discrete probability distribution
0:21 distribution
0:24 so on 4 millimeter nut and guys is
0:28 e of x which means the expected value
0:32 is equal to the summation of x
0:35 times f of x where x
0:39 is the element of the support
0:42 okay so let's have example number one
0:46 so let x be a discrete random variable
0:49 and s is equal to 0
0:52 1 2 3 be
0:56 its support so the probability must function
1:07 okay so as you notice in your acting
1:10 probability though is one for it
1:14 if x is element of s
1:17 which means your x naught n is zero
1:20 one two three okay
1:24 then the probability is zero if
1:27 otherwise okay or if x is not an
1:31 element of s so parabola solves nothing c
1:31 c
1:34 expected value nothing
1:37 submission x or x times f of
1:42 x so i've been adding summation guys
1:45 being a sum of all or even
1:48 or plus nothing x
1:52 times f of x okay
1:59 which is zero
2:02 so we have zero times
2:09 f of x so on f of x not n is one fourth
2:14 plus next nothing s is your one
2:22 plus two times
2:27 f of x which is one fourth
2:30 plus three you're adding last nine
2:34 x times one fourth
2:37 okay so simplifying nothing you know nothing
2:38 nothing
2:41 formula so zero times one fourth the
2:45 zero or cancel out plus one times one
2:47 fourth we have one
2:50 fourth plus two times one fourth this is
2:52 two over four
2:54 so the pokemon multiply line and whole
2:55 number to fraction
2:58 multiply like nothing you adding whole
3:00 number during the numerator
3:03 okay then copy the denominator
3:05 then three times one fourth this is three
3:06 three
3:10 over four okay
3:14 so simplify nothing so since
3:17 denominator so copy language in denominator
3:18 denominator
3:22 then 1 plus 2 plus 3
3:25 is equal to 6 or
3:28 this is 3 over 2
3:33 so in decimal number and this is 1.5
3:46 now however guys so let's have another example
3:47 example
3:51 number two so let x be a discrete random
3:53 variable with support as
3:56 one two three
4:00 where f of x is is equal to
4:03 1 over 6 times x if
4:06 x is an element of s so if it's a b
4:10 n 1 2 3 x
4:14 in volume adding a random variable
4:17 probability is one over six times
4:21 x okay then zero number
4:25 if otherwise okay then we asked to
4:26 compute for d
4:30 expected value no adding x
4:33 so again so using the same formula we have
4:34 have
4:37 the summation of x times f of
4:40 x okay
4:44 so it's a given at n and first value now
4:46 x naught and is one
4:50 times f of x which is one over six
4:55 x so on my action adding a probability
4:57 so unfortunate x nagina with nothing is one
4:58 one
5:01 okay so meaning multiply nothing see one
5:02 over six
5:05 by one
5:08 okay plus your next
5:12 value number x naught n which is two
5:17 times f of x which is one over six
5:20 x so on x nagina with nothing theta is two
5:26 okay plus three
5:30 times f of x which is one over six
5:38 okay now however guys so simplify nothing
5:40 nothing
5:43 so one times one over six times
5:52 plus two times one over
5:56 six this is two over six then times two
5:59 we have four over six
6:02 okay so again multiply time whole number
6:04 to fraction
6:07 numerator long time multiply then three times
6:08 times
6:11 one over six that is three over six
6:14 then times three that is
6:18 nine over six okay
6:21 so since uh we have common denominators
6:22 so bring down
6:26 nothingn then we have 1 plus 4
6:31 plus 9 which is 14.
6:35 so therefore the expected value
6:39 is equal to 7 over 3
6:52 okay so next let's have example number three
6:52 three
6:56 so find the expected value of
6:59 x so this time we have a discrete
7:02 probability distribution so we have six
7:05 random variables which is one
7:08 two three four five and six then your
7:11 probability in a minor adding a
7:14 random variable is we have point fifteen
7:32 random instead of using
7:36 uh x times f of x this time we have x
7:40 times p of x okay
8:06 x times p of x okay so you move to play
8:07 like that and see x
8:10 the answer i think corresponding p of
8:13 x so 1 times point 15
8:18 so we have uh 0.15
8:24 then 2 times 0.25 this is 0.50
8:27 3 times point thirty so this is point
8:31 ninety then four times fifty point fifteen
8:31 fifteen
8:35 we have zero point sixty then
8:38 five times point ten this is zero point
8:42 fifty then six times
8:45 point zero five we have zero point
8:49 thirty okay so after in yamagawa guys
8:50 you are adding
9:05 50 plus 0.90 plus
9:08 0.60 plus point fifty
9:12 plus point thirty we have the
9:15 two point ninety five
9:18 okay so it on two point ninety five eta
9:22 magicking expected
9:25 value all right
9:28 joba guys so this is the end of our video
9:29 video
9:32 i hope mina to tune in so if you have
9:34 questions or clarifications kindly put
9:36 them in the comment section
9:38 below so thank you guys for watching
9:39 this is prof d
