00:01
Hi everyone in this question we have given a sample of size 2 by using the numbers 1 2 3 4 5 6 with the replacement so i will list all the elements x1 and x2 with replacements i will write 1 1 1 2 1 3 1 4 1 5 and so on okay, so i have listed all of them so what i have to do is i have to evaluate sample mean now how i will evaluate the sample mean i will add both x1 and x2 divided by the 2 because the number we have taken is only 2 so we'll take the mean of that so i will evaluate all the mean sample mean and let you know so i have evaluated the sample mean by just adding the x1 plus x2 divided by 2 for each it every row for example 1 plus 1 divided by 2 that will give me 1 1 plus 2 is equal to 3 divided by 2 that will give me 1 .5 okay similarly i have evaluated all the sample mean okay for this thing okay now in the question we are asked to find the mean of the sample mean so what we will do is mean of the sample mean we can simply add all the sample mean that is nothing but how many times one came one time plus 1 .5 how many times it came 2 times so it will be 3 plus 2 how many times it came 3 times so it will be 6 okay similarly i have added all the the number of times 2 .5 repeats or the number of times 3 repeats or the number of times 3 .5 repeats and so on till 6.
02:20
I have multiplied them and it becomes easy for me to calculate.
02:26
So it becomes 1 plus 3 plus 6 plus 15 plus 10 plus 21 plus 20 plus 18 plus 15 plus 15 plus 15 plus 11 plus 6 and how many are there total total are 36 because for each there are 6 so how many numbers are given in the question is 1 2 3 4 5 6 so 6 into 6 is 36 so mean is actually the total adding all the numbers upon the number of the observation how many are there okay so what we will do and i have evaluated this numerator by simply seeing in the table, seeing in the table that how many times my one is coming, how many times my 1 .5 is coming, how many times 2 is repeating, how many times 2 .5 is repeating.
03:31
So it becomes easy for me to calculate.
03:34
If it is repeating 5 times, so i will directly multiply it by 5, 2 .5 into 5, and i will directly add it.
03:41
Okay, so this is how i evaluated this numerator.
03:47
So this sum becomes nothing but 1 .26.
03:56
So divided by 36, it becomes 3 .5.
04:03
So what i got mean of sample mean, which can be represented as e of x equal to that of 3 .5.
04:20
3 .5.
04:29
Okay, so now we got the mean.
04:36
Now we have to find the variance.
04:39
For evaluating variance, what we will do? variance is given by e of x squared minus e of x the whole square.
04:56
Now for evaluating e of x square what i have to do is i have to say simply squaring these all quantities which are there...