Don't understand Stats Prob: Let N be pos geometric random var....

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Joystar77

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Jul 8, 2013
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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).
 
Joystar77 said:
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).
Click to expand...


Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions e.g. define a positive geometric random variable.

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http://www.freemathhelp.com/forum/th...217#post322217
 
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