00:01
Ok, so we've got this pdf and firstly we're asked to find the value of c so that this is valid.
00:04
So all we need is that the sum of the probabilities for x to equal x and y to equal y over all the possible values is equal to 1.
00:14
And that's just the sum of all elements in this table, which we can find is equal to 12 over c.
00:20
And so we find that c equals 12.
00:23
Part b asks for the marginal distribution of x.
00:27
So we can see that x can take values 1, 2 and 3.
00:30
And the probability for it to take value 1 is just the sum of all the probabilities in the row of x equals 1 so that's going to be 2 over c which is 2 over 12 or equivalently 1 over 6.
00:44
Similarly for x equals 2 we can see that we're going to get 5 over 12 and the same for x equals 3.
00:51
Part c, what is the expected value and variance of x? the expected value is just given by the sum over all all the values that x can take, which is from 1 to 3, times the probability that it takes those values.
01:05
So here it would be 1 times the 6th plus 2 times 5 twelfths plus 3 times 5 twelfths.
01:10
And that gives us 2 .25.
01:15
Similarly, well, the variance is given by the expectation of x squared minus the expectation of x squared.
01:22
We have the expectation of x...