Homework SourseSupposeXN14YN21andZN23AssumeXYand Z are independent Find the
SupposeX~N(1,4),Y~N(2,1),andZ~N(2,3).AssumeX,Y,and Z are independent.
Find the distribution of
(a) X Y,
(b) X +Y2Z,
and
(c) X Y 2Z.
Solution
SupposeX~N(1,4),Y~N(2,1),andZ~N(2,3).AssumeX,Y,and Z are independent.
Find the distribution of
Mean of X-Y =1-2= -1
Variance of X-Y =4+1=5
X –Y ~ N(-1, 5)
Mean of X +Y2Z =1+2-2*2 = -1
Variance of X +Y2Z =4+1+4*3 =17
X +Y2Z ~ N(-1, 17)
and
(c) X Y 2Z.
Mean of X -Y2Z =1-2-2*2 = -5
Variance of X -Y2Z =4+1+4*3 =17
X -Y2Z ~ N(-5, 17)
