Answer to Question #331367 in Statistics and Probability for DepressedStudent

Question

Construct the sampling distribution

1. A population consists of the values 1,4,3,2 with sample size 2.

2. A population consists of 1,3,5,7,9 with sample size 3.

Answer 1

1. m(1,4)= (1+4)/2=2.5

m(1,3)=(1+3)/2=2

m(1,2)=(1+2)/2=1.5

m(2,3)=(2+3)/2=2.5

m(2,4)=(2+4)/2=3

m(3,4)=(3+4)/2=3.5

Frequency F(2)=F(1.5)=F(3)=F(3.5)=1

F(2.5)=2

Probability $P(x)=F(x)/\sum F(x)$

P(2)=P(1.5)=P(3)=P(3.5)=1/6

P(2.5)=2/6=1/3

2.

m(1,3,5)=(1+3+5)/3=3

m(1,3,7)=(1+7+3)/3=3.7

m(1,3,9)=(1+3+9)/3=4.3

m(1,5,9)=(1+5+9)/3=5

m(1,5,7)=(1+5+7)/3=4.3

m(1,7.9)=(1+7+9)/3=5.7

m(3,5,7)=(3+5+7)/3=5

m(3,5,9)=(3+5+9)/3=5.7

m(3,7,9)=(3+7+9)/3=6.3

m(5,7,9)=(5+7+9)/3=7

Frequency F(3)=F(3.7)=F(6.3)=F(7)=1

F(4.3)=F(5.7)=F(5)=2

Probabilitys $P(x)=F(x)/\sum F(x)$

P(3)=P(3.7)=P(6.3)=P(7)=0.1

P(4.3)=P(5.7)=P(5)=0.2