sneaky666
Oct31-10, 04:16 PM
1.
Let X~Geometric(1/4), and let Y have probability function:
pY(y)=
1/6 if y=2
1/12 if y=5
3/4 if y=9
0 otherwise
Let W=X+Y. Suppose X and Y are independent. Compute pW(w) for all w in R.
For this i am not sure i think its
summation from K=0 to infinity (PY=w-K)(1/4)(3/4)^K
where
(PY=w-K) = 1/6 if w-K=2
(PY=w-K) = 1/12 if w-K=5
(PY=w-K) = 3/4 if w-K=9
(PY=w-K) = 0 otherwise
Is this right?
2.
Suppose X has density fX(x)=(x^3)/4 for 0<x<2, otherwise fX(x)=0, and Y has density fY(y)=(5y^4)/32 for 0<y<2, otherwise fY(y)=0. Assume X and Y are independent, and let Z=X+Y.
Compute the density fZ(z) for Z.
For this is it
the integral from z-2 to 2 (x^3)/4 * (5(z-x)^4)/32 dx
Is this right?
Let X~Geometric(1/4), and let Y have probability function:
pY(y)=
1/6 if y=2
1/12 if y=5
3/4 if y=9
0 otherwise
Let W=X+Y. Suppose X and Y are independent. Compute pW(w) for all w in R.
For this i am not sure i think its
summation from K=0 to infinity (PY=w-K)(1/4)(3/4)^K
where
(PY=w-K) = 1/6 if w-K=2
(PY=w-K) = 1/12 if w-K=5
(PY=w-K) = 3/4 if w-K=9
(PY=w-K) = 0 otherwise
Is this right?
2.
Suppose X has density fX(x)=(x^3)/4 for 0<x<2, otherwise fX(x)=0, and Y has density fY(y)=(5y^4)/32 for 0<y<2, otherwise fY(y)=0. Assume X and Y are independent, and let Z=X+Y.
Compute the density fZ(z) for Z.
For this is it
the integral from z-2 to 2 (x^3)/4 * (5(z-x)^4)/32 dx
Is this right?