 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Mathematics course of the University of Oxford

Year 2 of the mathematics course of the University of Oxford

Options I course of the University of Oxford

Past exam of the options I course of the University of Oxford

2012

From the marginal density,
$$
\mathbb E X=12\int_0^1x^2(1-x)^2\,dx=\frac25,
\qquad\mathbb E Y=\frac25.
$$
The mixed moment is
$$
\mathbb E[XY]=\int_0^1\int_0^{1-x}24x^2y^2\,dy\,dx
=8\int_0^1x^2(1-x)^3\,dx=\frac2{15}.
$$
Thus the <covariance> is
$$
\boxed{\operatorname{Cov}(X,Y)=\frac2{15}-\frac4{25}=-\frac2{75}.}
$$
The negative sign is consistent with the support constraint: a large value of one variable leaves a smaller available range for the other.

Solution

Past exam of the options I course of the University of Oxford / 2012 / M / M2 / b / iii / Solution

Past exam of the options I course of the University of Oxford / 2012 / M / M2 / b / iii / Solution

 Ancestors (14)

 Discussion (0) New discussion

 Articles by others on the same topic (0)

Past exam of the options I course of the University of Oxford / 2012 / M / M2 / b / iii / Solution

 Ancestors (14)

 Discussion (0)  Subscribe (1) New discussion

 Articles by others on the same topic (0)

 Discussion (0) New discussion