00:01
Hi, i'm david and i'm here to help you answer your question.
00:04
Now let me bring up your question here.
00:09
Now in this question we are considered the john distribution on the two random variables.
00:15
Here we have a fair cone is tossed three times.
00:21
And let's try to list all of the sample space for the three times here.
00:26
We can have the hat, hat, hat, hat, tail.
00:35
We can have the hat tail hat then tell hat and then we can have the head tail tail the tail the tail hat tell the tail hat then we can have the tell tell tell tell so totally we have eight outcomes there now let you find the x it will be the number of the hat on the head on the second and the third toss and the y it will be the number of the hat on the three tosses so let's try to make the john distribution of the x and the y now so we have here will be the x this will be the y now why it will have the value can be will be 0 1 2 and 3 x can have only the value 0, 1 and 2.
01:49
Now we see the total outcomes will be 8, so every time we count we need to divide by 8.
01:54
Now we have the 0 for x and 0 for y means that there's no head for the y, no head for the x and the only outcomes there must be the tell, tell, tell.
02:09
And then we will have only one case here.
02:13
So the answer for the first one, it will be the one out of.
02:20
This one will be one out of eight.
02:23
And now for the second one, we will have, it will equal to, this one is not, it will be one out of eight.
02:36
This one will be the tell, tell, tell.
02:38
To get the tell, tell, tell, we will have, let's say it's a fair con.
02:42
So, you know, to get the probability will be one after two times one out of two.
02:47
Times 1 out of 2 then we will have this one will be 1 out of 8 and yes that would be 2 times 2 will be 4 4 times 2 will be 8 so that makes sense here and now the next one we will have when x equal to 0 and y equal to 1 and in it you have that and then we only have the option to have the hat and then this one that will be the case where we have the zero hat on the second and the third thoughts and one hat from the tail.
03:25
So therefore this only be one out of eight here...