Three randomly selected households are surveyed. The numbers of people in the households are
11,
22,
and
1212.
Assume that samples of size
nequals=2
are randomly selected with replacement from the population of
11,
22,
and
1212.
Listed below are the nine different samples. Complete parts (a) through (c).
11,11
11,22
11,1212
22,11
22,22
22,1212
1212,11
1212,22
1212,1212
a. Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values.
s2 
Probability 


0 0.3 1 0 
nothing 

1 25 1 0.5 
nothing 

▼ 25 50 100 
nothing 

▼ 60.5 30.3 121 
nothing 
please show me a step by step to the answer
let first sample is x1 and 2nd sample is x2
x1  x2  s^{2}  
1  1  0  
2  1  0.5  
12  1  60.5  
1  2  0.5  
2  2  0  
12  2  50  
1  12  60.5  
2  12  50  
12  12  0 
for 1st sample (1,1) , mean =(1+1)/2=1 ; therefore variance =(xxbar)^{2}/(n1)
=((11)^2+(11)^2)/(21)=0
for 2nd sample (2,1) mean =(2+1)/2=1.5 ; therefore variance =(xxbar)^{2}/(n1)
=((21.5)^2+(11.5)^2)/(21)=0.5
all other sample variance can be calculated in above manner:
therefore"
s2  probability 
0  1/3 
0.5  2/9 
50  2/9 
60.5  2/9 
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