Find the value of c such that the function f ( x , y ) = c ( x + y ) for 0 < x < 3 and 0 < y < x satisfies the properties of a joint probability density function. Compute P ( X < 1 , Y < 2 ) .

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Answer 1

Question

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

b.

To determine

Compute P(1<X<2).

c.

To determine

Compute P(Y>1).

d.

To determine

Compute P(X<2,Y<2).

e.

To determine

Compute E(X).

f.

To determine

Compute E(Y).

g.

To determine

Find marginal probability distribution of X.

h.

To determine

Find the conditional probability distribution of Y given that X=1.

i.

To determine

Find E(Y|X=1).

j.

To determine

P(Y>2|X=1).

k.

To determine

Find the conditional probability distribution of X given that Y=2.

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Using the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416plus+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. Square Feet Market Value1813 911001916 1043001842 934001814 909001836 1020002030 1085001731 877001852 960001793 893001665 884001852 1009001619 967001690 876002370 1139002373 1131001666 875002122 1161001619 946001729 863001667 871001522 833001484 798001589 814001600 871001484 825001483 787001522 877001703 942001485 820001468 881001519 882001518 885001483 765001522 844001668 909001587 810001782 912001483 812001519 1007001522 872001684 966001581 86200

Answer 2

Question

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

b.

To determine

Compute P(1<X<2).

c.

To determine

Compute P(Y>1).

d.

To determine

Compute P(X<2,Y<2).

e.

To determine

Compute E(X).

f.

To determine

Compute E(Y).

g.

To determine

Find marginal probability distribution of X.

h.

To determine

Find the conditional probability distribution of Y given that X=1.

i.

To determine

Find E(Y|X=1).

j.

To determine

P(Y>2|X=1).

k.

To determine

Find the conditional probability distribution of X given that Y=2.

Expert Solution & Answer

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Answer 3

Question

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

b.

To determine

Compute P(1<X<2).

c.

To determine

Compute P(Y>1).

d.

To determine

Compute P(X<2,Y<2).

e.

To determine

Compute E(X).

f.

To determine

Compute E(Y).

g.

To determine

Find marginal probability distribution of X.

h.

To determine

Find the conditional probability distribution of Y given that X=1.

i.

To determine

Find E(Y|X=1).

j.

To determine

P(Y>2|X=1).

k.

To determine

Find the conditional probability distribution of X given that Y=2.

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Answer 4

Question

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

b.

To determine

Compute P(1<X<2).

c.

To determine

Compute P(Y>1).

d.

To determine

Compute P(X<2,Y<2).

e.

To determine

Compute E(X).

f.

To determine

Compute E(Y).

g.

To determine

Find marginal probability distribution of X.

h.

To determine

Find the conditional probability distribution of Y given that X=1.

i.

To determine

Find E(Y|X=1).

j.

To determine

P(Y>2|X=1).

k.

To determine

Find the conditional probability distribution of X given that Y=2.

Expert Solution & Answer

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Answer 5

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

b.

To determine

Compute P(1<X<2).

c.

To determine

Compute P(Y>1).

d.

To determine

Compute P(X<2,Y<2).

e.

To determine

Compute E(X).

f.

To determine

Compute E(Y).

g.

To determine

Find marginal probability distribution of X.

h.

To determine

Find the conditional probability distribution of Y given that X=1.

i.

To determine

Find E(Y|X=1).

j.

To determine

P(Y>2|X=1).

k.

To determine

Find the conditional probability distribution of X given that Y=2.

Answer 6

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

Answer 7

Chapter 5.1, Problem 15E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).

Answer 8

b.

To determine

Compute P(1<X<2).

Answer 9

b.

To determine

Compute P(1<X<2).

Answer 10

c.

To determine

Compute P(Y>1).

Answer 11

c.

To determine

Compute P(Y>1).

Answer 12

d.

To determine

Compute P(X<2,Y<2).

Answer 13

d.

To determine

Compute P(X<2,Y<2).

Answer 14

e.

To determine

Compute E(X).

Answer 15

e.

To determine

Compute E(X).

Answer 16

f.

To determine

Compute E(Y).

Answer 17

f.

To determine

Compute E(Y).

Answer 18

g.

To determine

Find marginal probability distribution of X.

Answer 19

g.

To determine

Find marginal probability distribution of X.

Answer 20

h.

To determine

Find the conditional probability distribution of Y given that X=1.

Answer 21

h.

To determine

Find the conditional probability distribution of Y given that X=1.

Answer 22

i.

To determine

Find E(Y|X=1).

Answer 23

i.

To determine

Find E(Y|X=1).

Answer 24

j.

To determine

P(Y>2|X=1).

Answer 25

j.

To determine

P(Y>2|X=1).

Answer 26

k.

To determine

Find the conditional probability distribution of X given that Y=2.

Answer 27

k.

To determine

Find the conditional probability distribution of X given that Y=2.

Answer 28

Expert Solution & Answer

Answer 29

Expert Solution & Answer

Answer 30

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Answer 31

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Find the value of c such that the function f ( x , y ) = c ( x + y ) for 0 &lt; x &lt; 3 and 0 &lt; y &lt; x satisfies the properties of a joint probability density function. Compute P ( X &lt; 1 , Y &lt; 2 ) .

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function. Compute P(X<1,Y<2).

Compute P(1<X<2).

Compute P(Y>1).

Compute P(X<2,Y<2).

Compute E(X).

Compute E(Y).

Find marginal probability distribution of X.

Find the conditional probability distribution of Y given that X=1.

Find E(Y|X=1).

P(Y>2|X=1).

Find the conditional probability distribution of X given that Y=2.

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Chapter 5 Solutions

Find the value of c such that the function f ( x , y ) = c ( x + y ) for 0 < x < 3 and 0 < y < x satisfies the properties of a joint probability density function. Compute P ( X < 1 , Y < 2 ) .

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and 0<y<x satisfies the properties of a joint probability density function.

Compute P(X<1,Y<2).