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I already fill the table for question 1. i hope someone expert can help me find answer for questions 2.

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Answer #1

(a.i.) frequency distribution of X and Y

X	frequency
1	4
2	3
2	5
Y	frequency
1	6
2	6

(a.ii.) joint probability distribution of X and Y

			X
		1	2	3	total
Y	1	0.1667	0.0833	0.2500	0.5000
	2	0.1667	0.1667	0.1667	0.5000
	total	0.3333	0.2500	0.4167	1.0000

(b) P(X=2|Y=1)=P(X=2 and Y=1)/P(Y=1)=0.0833/0.5=0.1667 and P(X=2)=0.25

here P(X=2) is greater than P(X=2|Y=1)

(c)Yes, number of pages are related to language used in the book

E(X)=sum(x*P(x))=1*0.3333+2*0.2500+3*0.4167=2.0834

E(Y)=sum(y*P(y))=1*0.5+2*0.5=1.5

E(XY)=sum(x*y*P(xy))=1*1*0.1667+1*2*0.0833+1*3*0.25+2*1*0.1667+2*2*0.1667+2*3*0.1667=3.0837

E(X)*E(Y)=2.0834*1.5=3.1251 which is not equal to E(XY)=3.0837, so X and Y are not independent and conclude that number of pages are related to language used in the book

following information has been generated when x is in ascending order for answering the above question

Y	x	X
1	20	1
2	22	1
1	28	1
2	32	1
2	39	2
2	42	2
1	45	2
2	48	3
1	52	3
2	71	3
1	72	3
1	72	3
$\bar{x}$	45.25
20%of $\bar{x}$	9.05
$\bar{x}$- 20%of $\bar{x}$	36.2
$\bar{x}$+20%of $\bar{x}$
	54.3

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Answer 1

(a.i.) frequency distribution of X and Y

X	frequency
1	4
2	3
2	5
Y	frequency
1	6
2	6

(a.ii.) joint probability distribution of X and Y

			X
		1	2	3	total
Y	1	0.1667	0.0833	0.2500	0.5000
	2	0.1667	0.1667	0.1667	0.5000
	total	0.3333	0.2500	0.4167	1.0000

(b) P(X=2|Y=1)=P(X=2 and Y=1)/P(Y=1)=0.0833/0.5=0.1667 and P(X=2)=0.25

here P(X=2) is greater than P(X=2|Y=1)

(c)Yes, number of pages are related to language used in the book

E(X)=sum(x*P(x))=1*0.3333+2*0.2500+3*0.4167=2.0834

E(Y)=sum(y*P(y))=1*0.5+2*0.5=1.5

E(XY)=sum(x*y*P(xy))=1*1*0.1667+1*2*0.0833+1*3*0.25+2*1*0.1667+2*2*0.1667+2*3*0.1667=3.0837

E(X)*E(Y)=2.0834*1.5=3.1251 which is not equal to E(XY)=3.0837, so X and Y are not independent and conclude that number of pages are related to language used in the book

following information has been generated when x is in ascending order for answering the above question

Y	x	X
1	20	1
2	22	1
1	28	1
2	32	1
2	39	2
2	42	2
1	45	2
2	48	3
1	52	3
2	71	3
1	72	3
1	72	3
$\bar{x}$	45.25
20%of $\bar{x}$	9.05
$\bar{x}$- 20%of $\bar{x}$	36.2
$\bar{x}$+20%of $\bar{x}$
	54.3