00:01
Hello everyone.
00:02
So here let x be the total number of tails and y be the total number of hex on the last flip.
00:17
So let us make a table for outcomes x, y and p of x comma y.
00:28
So outcomes for ht, h h h h t and t.
00:38
So x value is 1, 0, 1, 2 and this is 0 1, 1, 1, 0 .0.
00:49
And this is 1 divided by 4, 1 divided by 4, 1 divided by 4 and 1 divided by 4.
00:56
So now if we see that p of x is equal to 1 comma y is equal to 0 is equals to 1 divided by 4 and p of x is equal to 0 comma y is equals to 1 is equal to 1 divided by 4 and p of x is equal to 2 comma y is equal to 0 this is also 1 divided by 4 and p of x is equal to 1 comma y is equals to 1 is equal to 1 divided by 4 so now the joint distribution of x y the joint distribution table if we make then we'll get this is 0 1 2 0 1 divided by 4 1 divided by 4 1 divided by 4 1 divided by 4 1 divided by 4 1 divided by 4 1 1 divided by 4 and 0.
02:12
P of x is 1 divided by 4, 1 divided by 4 and 1 divided by 4.
02:18
So, p of y is equal to 1 divided by 2 and 1 divided by 2.
02:25
So here p of x and p of y are the marginal distributions of x and y respectively.
02:32
So this is the answer for the a part.
02:34
Now coming to the b part, now the marginal distribution of x, marginal distribution of x for x and p of x we'll get this is 0 1 2 and p of x will get this is 0 1 2 and p of x will get 1 divided by 4 1 divided by 2 and 1 divided by 4 in the same way marginal distribution of y and here we have 0 and 1 and 1 this is 1 divided by 2 and 1 divided by 2.
03:28
This is the answer for the b part.
03:31
Now in the c part, p xy where x given y is equal to 1.
03:41
So here x given y and p of x given y is equal to 1...