The severity of a certain cancer is designated by one of the grades 1,2,3,4 with 1 being the least severe and 4 the most severe. If X is the score of an initially diagnosed patient and Y the score of that patient after three months of treatment, hospital data indicates that p ( i , j ) P ( X = i , Y = j ) is given by p ( 1 , 1 ) = .08 , p ( 1 , 2 ) = .06 , p ( 1 , 3 ) = .04 , p ( 1 , 4 ) = .02 p ( 2 , 1 ) = .06 , p ( 2 , 2 ) = .12 , p ( 2 , 3 ) = .08 , p ( 2 , 4 ) = .04 p ( 3 , 1 ) = .03 , p ( 3 , 2 ) = .09 , p ( 3 , 3 ) = .12 , p ( 3 , 4 ) = .06 p ( 3 , 1 ) = .01 , p ( 4 , 2 ) = .03 , p ( 4 , 3 ) = .07 , p ( 4 , 4 ) = .09 a. Find the probability mass functions of X and of Y; b. Find E[X] and E[Y]. c. Find Var (X) and Var (Y).
The severity of a certain cancer is designated by one of the grades 1,2,3,4 with 1 being the least severe and 4 the most severe. If X is the score of an initially diagnosed patient and Y the score of that patient after three months of treatment, hospital data indicates that p ( i , j ) P ( X = i , Y = j ) is given by p ( 1 , 1 ) = .08 , p ( 1 , 2 ) = .06 , p ( 1 , 3 ) = .04 , p ( 1 , 4 ) = .02 p ( 2 , 1 ) = .06 , p ( 2 , 2 ) = .12 , p ( 2 , 3 ) = .08 , p ( 2 , 4 ) = .04 p ( 3 , 1 ) = .03 , p ( 3 , 2 ) = .09 , p ( 3 , 3 ) = .12 , p ( 3 , 4 ) = .06 p ( 3 , 1 ) = .01 , p ( 4 , 2 ) = .03 , p ( 4 , 3 ) = .07 , p ( 4 , 4 ) = .09 a. Find the probability mass functions of X and of Y; b. Find E[X] and E[Y]. c. Find Var (X) and Var (Y).
The severity of a certain cancer is designated by one of the grades 1,2,3,4 with 1 being the least severe and 4 the most severe. If X is the score of an initially diagnosed patient and Y the score of that patient after three months of treatment, hospital data indicates that
p
(
i
,
j
)
P
(
X
=
i
,
Y
=
j
)
is given by
p
(
1
,
1
)
=
.08
,
p
(
1
,
2
)
=
.06
,
p
(
1
,
3
)
=
.04
,
p
(
1
,
4
)
=
.02
p
(
2
,
1
)
=
.06
,
p
(
2
,
2
)
=
.12
,
p
(
2
,
3
)
=
.08
,
p
(
2
,
4
)
=
.04
p
(
3
,
1
)
=
.03
,
p
(
3
,
2
)
=
.09
,
p
(
3
,
3
)
=
.12
,
p
(
3
,
4
)
=
.06
p
(
3
,
1
)
=
.01
,
p
(
4
,
2
)
=
.03
,
p
(
4
,
3
)
=
.07
,
p
(
4
,
4
)
=
.09
a. Find the probability mass functions of X and of Y;
b. Find E[X] and E[Y].
c. Find Var (X) and Var (Y).
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Precalculus: Mathematics for Calculus - 6th Edition
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