00:01
So this question, we're told that we flip a balance coin three times.
00:12
Now, x is the number of heads, and y is the number of heads minus the number of tails.
00:27
But remember that the number of heads is x, so y equals x minus.
00:33
But the number of tails is the number of flips minus the number of heads, so 3 minus x.
00:39
So y is 2x minus 3.
00:44
So now we want a table showing the joint probability distribution.
00:51
Well, so x can be 0, 1, 2 or 3, in which case y will be 2x minus 3, so minus 3, 2 minus 3, 4 minus 3 is 1, 6 minus 3 is 1, 6 minus 3 is 3.
01:17
And the probability that x equals x and y equals y well x is the number of heads so x is going to be binomially distributed we're told there's three flips and we're told that it's a fair coin so that means there's a half chance of getting ahead each time and that means the probability x equals x is equal to three choose x a half to the x and then a half of the 3 minus x, that's just a half cubed...