00:01
So, here we have been given that a fair coin is tossed three times.
00:12
Here x denotes the number of heads among the first two tosses whereas y represents the number of heads among the last two tosses.
00:44
We have to find the variance of x.
00:49
So, if we see the sample space in this experiment, so it is that head, head, head appears on the all three coins when they are tossed three times or head, head, tail, head, tail, head, head, tail, tail, tail, head, head, tail, head, tail, tail, head and tail, tail, tail.
01:25
So this is the sample space.
01:28
Now we can see that x can be 0 ,1 ,2.
01:37
Similarly y can also be 0 ,1 ,2 and we already know x and y represents the number of heads among the first two and last two tosses.
01:48
So here if we draw this table where here we have been given with x and y which are 0 ,1 ,2.
02:05
Here is the probability of y.
02:09
Now here also there are 0 ,1 and 2 and if we see then here we have probability of x.
02:25
So when we continue this table here in this case it will be 1 by 8 which means 0 appears as x and y which means there are number of heads as 0 on the first two and last two coins.
02:55
So it appears only one time so the probability is 1 by 8.
02:58
Here also it is 1 by 8...