Let N be a positive geometric random variable (P(N = j) = p(1 p)
j1
, j = 1; 2; : :
and let the distribution of T given N = n be gamma with parameter n (given N = n,
T has density proportional to x
n1
e
x
).
(a) Without computing the density of T, can you nd ET?
(b) What is the joint distribution of (T; N)?
(c) What is the density of T? Use the density to compute ET and check that it agrees
with your answer in part (a).
j1
, j = 1; 2; : :
and let the distribution of T given N = n be gamma with parameter n (given N = n,
T has density proportional to x
n1
e
x
).
(a) Without computing the density of T, can you nd ET?
(b) What is the joint distribution of (T; N)?
(c) What is the density of T? Use the density to compute ET and check that it agrees
with your answer in part (a).