Answer to Question #333130 in Statistics and Probability for Geeeee

Question

Samples of four cards are drawn at random from a population of eight cards numbered from 1 to 6.

A. How many possible samples can be drawn?

B. Construct the sampling distribution of sample means.

Answer 1

a. $C^4_6=\frac{6!}{4!2!}=15$

b.m(1,2,3,4)=(1+2+3+4)/4=2.5

m(1,2,3,5)=(1+2+3+5)/4=2.75

m(1,2,3,6)=(1+2+3+6)/4=3

m(1,2,4,5)=(1+2+4+5)/4=3

m(1,2,4,6)=(1+2+4+6)/4=3.25

m(1,2,5,6)=(1+2+5+6)/4=3.5

m(1,3,4,5)=(1+3+4+5)/4=3.25

m(1,3,4,6)=(1+3+4+6)=3.5

m(1,3,5,6)=m(1+3+5+6)/4=3.75

m(1,4,5,6)=(1+4+5+6)/4=4

m(2,3,4,5)=(2+3+4+5)/4=3.5

m(2,3,4,6)=(2+3+4+6)/4=3.75

m(2,3,5,6)=(2+3+5+6)/4=4

m(2,4,5,6)=(2+4+5+6)/4=4.25

m(3,4,5,6)=(3+4+5+6)/4=4.5

Frequencies F(2.5)=F(2.75)=F(4.25)=F(4.5)=1

F(3)=F(3.25)=F(3.75)=F(4)=2

F(3.5)=3

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

P(2.5)=P(2.75)=P(4.25)=P(4.5)=1/15

P(3)=P(3.25)=P(3.75)=P(4)=2/15

P(3.5)=3/15=1/5