(7) Find the marginal density of X when the conditional density of X given {Y = y} is Poisson(y) and the marginal density of Y is G(A, a). Here, A, a > 0 are fixed numbers. Follow the following two steps. By the TTP write an expression for P(X = k) when k = 0,1,2,-... (i1) Simplify the expression by performing the integration/summation. For step () the following expressions are proposed for the marginal density of X. (a) P(X = k) = L P(X = k,Y = y) dy = * dy. (b) P(X = k) = S P(X = k,Y = y) fr(y) dy = yley dy. T(a) (c) P(X = k) = f® P(X = k|Y = y) fr(y) dy = (d) P(X = k) = P(X = k|Y = y)/fr (y) dy = * yley dy. r(a) - (e) None of the above (a) (b) (c) (d) (e) N/A (i- Select One)
(7) Find the marginal density of X when the conditional density of X given {Y = y} is Poisson(y) and the marginal density of Y is G(A, a). Here, A, a > 0 are fixed numbers. Follow the following two steps. By the TTP write an expression for P(X = k) when k = 0,1,2,-... (i1) Simplify the expression by performing the integration/summation. For step () the following expressions are proposed for the marginal density of X. (a) P(X = k) = L P(X = k,Y = y) dy = * dy. (b) P(X = k) = S P(X = k,Y = y) fr(y) dy = yley dy. T(a) (c) P(X = k) = f® P(X = k|Y = y) fr(y) dy = (d) P(X = k) = P(X = k|Y = y)/fr (y) dy = * yley dy. r(a) - (e) None of the above (a) (b) (c) (d) (e) N/A (i- Select One)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:(7) Find the marginal density of X when the conditional density of X given {Y = y} is Poisson(y) and the marginal density of Y is G(A, a). Here, 1, a > 0 are fixed numbers. Follow the following two steps.
(i) By the TTP write an expression for P(X = k) when k = 0,1,2,-...
(ii) Simplify the expression by performing the integration/summation.
For step (i) the following expressions are proposed for the marginal density of X.
(a) P(X = k) = * P(X = k,Y = y) dy = dy.
(b) P(X = k) = ° P(X = k,Y = y) fy (y) dy = ya le v dy.
e Vyk
(c) P(X = k) = P(X = k|Y = y) fr (y) dy = A y"-le-Ay dy.
T(a)
e Yyk
(d) P(X = k) = P(X = k|Y = y)/ fr(y) dy = /A ya-le Ay dy.
(e) None of the above
(a)
(b)
(c)
(d)
(e)
N/A
(i- Select One)
For step (ii) the following expressions are proposed for the marginal density of X.
(a) P(X = k) = (A
k = 0,1, 2, --.
(b) P(X = k) =
k = 0, 1, 2, -..
(금) (금).
A ), k= 0,1, 2, -.
(c) P(X = k) =
k = 0,1,2, ...
(d) P(X = k) =
(1+a)k+1
(e) None of the above
(a)
(b)
(c)
(d)
(e)
N/A
(ii- Select One)
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