QI A random sample of n=2 households was drawn from a small colony N=5 households having monthly income (in rupees) as follows Households: 3 4 5 Income (in thousand rupees): 8 6.5 7.5 7 a) Calculate population mean Y , variance o? and s b) Enumerate all possible samples of size n=2 by without replacement method and verify that i) Sample mean is an unbiased estimator of population mean ii) Nỹ is an unbiased estimate of population total Y ii) V(ỹ) = (N-n)S and nN iv) E(s³)= s? Q2 In a population N=5, the values are 2, 4, 6, 8 and 10 then for a SRS of size n=3 show that V (y) srsworV(y) srswr

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Q1
A random sample of n=2 households was drawn from a small colony N=5 households
having monthly income (in rupees) as follows
Households:
1 2 3
4
5
Income (in thousand rupees):
8
6.5
7.5
7
6.
a) Calculate population mean Y , variance o² and s?
b) Enumerate all possible samples of size n=2 by without replacement method and verify that
i)
Sample mean is an unbiased estimator of population mean
ii)
Nỹ is an unbiased estimate of population total Y
(N -n)S?
-and
iii)
V(ỹ) =
nN
iv)
E(s³)= s?
Q2
In a population N=5, the values are 2, 4, 6, 8 and 10 then for a SRS of size n=3 show that
V (y) srsworV (y) srswr
Transcribed Image Text:Q1 A random sample of n=2 households was drawn from a small colony N=5 households having monthly income (in rupees) as follows Households: 1 2 3 4 5 Income (in thousand rupees): 8 6.5 7.5 7 6. a) Calculate population mean Y , variance o² and s? b) Enumerate all possible samples of size n=2 by without replacement method and verify that i) Sample mean is an unbiased estimator of population mean ii) Nỹ is an unbiased estimate of population total Y (N -n)S? -and iii) V(ỹ) = nN iv) E(s³)= s? Q2 In a population N=5, the values are 2, 4, 6, 8 and 10 then for a SRS of size n=3 show that V (y) srsworV (y) srswr
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