Question
Suppose that the joint Pd f of and y is grven by f(x, y)={1 / 6(4-2 x-y) x geq 0 y geq 0. a) determine the conditional pdf of y given x
Solution
4.7
(287 Votos)
Zulmira
Mestre · Tutor por 5 anos
Resposta
To determine the conditional probability density function (pdf) of
given
, we need to integrate the joint pdf \( f(x, y) \) with respect to
over the range where
is defined.Given the joint pdf:
The range for
is
.The conditional pdf of
given
is:
First, we need to find the marginal pdf \( f(x) \) by integrating the joint pdf \( f(x, y) \) with respect to
over the range
:
Substitute \( f(x, y) \):
\[ f(x) = \frac{