a = 0
b = 8
c = 8
d = 0
e = 3
f = 8
Suppose that X is uniformly distributed on the interval [3,8] , and that given X=x , Y is uniformly distributed on the interval [0,x] . That is, the conditional PDF of Y given X=x is
fY|X(y|x)=1/x, 0≤y≤x.
Find the PDF fY(y) of Y . It will take the form
fY(y)=⎧⎩⎨aln(b)
aln(c/y)
0]y∈[e,f]otherwise.
Answer by finding a,b,c,d,e,f , where d<e<f .
Recall: If 0≤a<b, then ∫ba 1/xdx=ln(ba) .
a=?
b=?
c=?
d=?
e=?
f=?
3 answers
a = 1/5
b = 0
c = 3
d = 1
e = 3
f = 8
b = 0
c = 3
d = 1
e = 3
f = 8
Continue from the problem above, i.e. X and Y are defined as above.
Calculate P(|X−Y|≤1).
(Enter an exact expression or in decimal accurate to at least 3 decimal places. To be accurate enough, use exact answers from the previous part.)
P(|X−Y|≤1)=
Calculate P(min(X,Y)≤6).
(Enter an exact expression or in decimal accurate to at least 3 decimal places.)
P(min(X,Y)≤6)=
Calculate P(|X−Y|≤1).
(Enter an exact expression or in decimal accurate to at least 3 decimal places. To be accurate enough, use exact answers from the previous part.)
P(|X−Y|≤1)=
Calculate P(min(X,Y)≤6).
(Enter an exact expression or in decimal accurate to at least 3 decimal places.)
P(min(X,Y)≤6)=
3 answers