This is a detailed solution based on Probability Theory of ISI MStat 2015 PSB Problem B5, with the prerequisites mentioned explicitly. Stay tuned for more.
Suppose that and
are random variables such that
Var
Var
(a) Evaluate Cov.
(b) Show that .
(c) If in addition, it is given that is bivariate normal, calculate E
.
(a)
Using , we use Var
- Var
=
.
(b)
Say
.
.
Do you remember the Cauchy - Schwartz Inequality?
. Hence,
.
(c)
and
.
is bivariate normal
~
.
.
This is a detailed solution based on Probability Theory of ISI MStat 2015 PSB Problem B5, with the prerequisites mentioned explicitly. Stay tuned for more.
Suppose that and
are random variables such that
Var
Var
(a) Evaluate Cov.
(b) Show that .
(c) If in addition, it is given that is bivariate normal, calculate E
.
(a)
Using , we use Var
- Var
=
.
(b)
Say
.
.
Do you remember the Cauchy - Schwartz Inequality?
. Hence,
.
(c)
and
.
is bivariate normal
~
.
.