00:01
We are given these two data set.
00:04
So what we have to find, we have to find the mean and the standard deviation.
00:09
For probable distributions, the mean is equal to, let me just recall the formula, which is this is sum of x times p of x and the standard deviation.
00:19
That is equal to this is expected value of.
00:22
So we can also call the mean as the expected value here.
00:27
Expected value of x squared and minus mu squared or let me just write this way so these are the two formula that we have to use for the standard deviation and also for the mean value let's first of all let's start with x times pfx for the first data 0 .0 times 0 .16 which is 0 .1 times 0 .27 which is 0 .27 and 2 times 0 .39 which is 0 .78 and 3 times this which is 0 .54.
01:06
So if i add all these values so we will get the expected value here which is 0 .27 plus 0 .78 plus 0 .54.
01:20
That is equal to 1 .59.
01:22
And what about for the standard deviation? so what we need, we need the expected value of x squared.
01:29
So we can get the expected value of x squared as this one.
01:33
Let me just write here, which is equal to this is x squared times p of x.
01:38
And this is, i mean, the sum of x squared times p of x.
01:42
So what we need, we need the x squared and then the x squared times p of x.
01:46
Let's do all the calculation here.
01:49
X squared is zero squared is zero.
01:51
One squared is one, two squared is four, and three squared is nine.
01:54
So the p .ofaxe is 0 .16, 0 .16, which is 0 .1, 1 times 0 .27, 4 times this value, which is 0 .39 times 4, which is equal to 1 .56, and 0 .54 times 9, that is equal to 4 .86.
02:21
So again, we have to just add all the values here.
02:25
This is 0 .4 .86 plus 1 .56 plus 0 .27, that is equal to 6 .69.
02:37
So the standard deviation, which is equal to the sum of the x squared and minus x squared.
02:55
So the sum of the x squared, which is 6 .69, minus, this is 1 .59 squared, which is 6 .69 minus, this is 1 .59 squared, which is equal to 4 .162.
03:16
So 162.
03:17
That is the answer for the standard division.
03:20
And we got the mean score.
03:21
Let me just write separately, which is the expected value of x.
03:24
That is equal 1 .59.
03:28
And for the next table, just follow the same process.
03:31
The first one is the x times pfx, which is equal to it.
03:35
This is 6 times 0 .40, which is 2 .40, and 0 .26 times 7, which is 1.
03:45
This is 82, and this is 1 .68.
03:51
17.
03:52
Let me just check the last one.
03:56
Yes, great...