Find the value of c such that the function f ( x , y ) = c ( x + y ) for 0 < x < 3 and x < y < x + 2 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 14E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and x<y<x+2 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 V(X).

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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Let Y₁, Y2,, Yy be random variables from an Exponential distribution with unknown mean 0. Let Ô be the maximum likelihood estimates for 0. The probability density function of y; is given by P(Yi; 0) = 0, yi≥ 0. The maximum likelihood estimate is given as follows: Select one: = n Σ19 1 Σ19 n-1 Σ19: n² Σ1

Please could you help me answer parts d and e. Thanks

Answer 2

Question

Chapter 5.1, Problem 14E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and x<y<x+2 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 V(X).

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 14E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and x<y<x+2 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 V(X).

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 4

Question

Chapter 5.1, Problem 14E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and x<y<x+2 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 V(X).

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 14E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and x<y<x+2 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 V(X).

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 14E

a.

To determine

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

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

Answer 7

Chapter 5.1, Problem 14E

a.

To determine

Find the value of c such that the function f(x,y)=c(x+y) for 0<x<3 and x<y<x+2 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 V(X).

Answer 17

f.

To determine

Compute V(X).

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 x &lt; y &lt; x + 2 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 x<y<x+2 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 V(X).

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 x < y < x + 2 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 x<y<x+2 satisfies the properties of a joint probability density function.

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