This document discusses simple random sampling. It begins by defining simple random sampling as selecting a sample from a population where each individual has an equal probability of being selected at each stage of sampling. It then discusses two common methods for obtaining a simple random sample: the lottery method and using a random number table. The document also explains the difference between simple random sampling with replacement (SRSWR), where selected units are replaced before subsequent selections, and simple random sampling without replacement (SRSWOR), where selected units are not replaced. It provides formulas for calculating the probability of selecting a given unit at a given draw for both SRSWR and SRSWOR.

1. Simple Random Sampling
Mr. Surajkumar D. Chaudhari
M.Sc. (Statistics), Sem – II, Roll no. : 03
Paper-203 (Sampling Theory)
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2. CONTENTS
• Introduction
• Why Simple Random Sampling?
• Method to get Simple Random Sample
• SRSWR
• SRSWOR
• Pir
(Probability of ith
unit to be selected at rth
draw)
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3. INTRODUCTION
• A Simple Random Sample is a set of individual
units chosen from a large Population.
• In Sample , each individual is chosen randomly
and all individual have same probability to be
selected in the sample at any stage during
Sampling process.
• This process and TECHNIQUE is known as
Simple Random Sampling.
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4. Why Simple Random Sampling?
• The members of the sample are selected
randomly.
• Every member has an equal chance of being
selected in the sample.
• Simple Random Sampling is a suitable
technique for a Population which is highly
homogeneous And having complete
sampling frame And having finite number of
units in the population.
• It is a Simplest way to get Random Sample.
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5. Method to get Simple Random
Sample
• There are two ways to get a Simple Random
Sample:
1. The Lottery Method
2. Random Number Table
• (1) The Lottery Method :
• First we give unique no. to all population units.
Like 1,2,…
• Each number placed in a card of Similar Size,
Similar Shape and Same Colour.
• All cards put in a bowl and mixed well.
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6. • Then Blindfolded person select a one card, and
note down that number written in the selected
card.
• Repeat this process till we reach the desired
Sample Size.
• (2) Random Number Table :
• A Random number table is a series of digits 0 to
9 arranged randomly in rows and columns.
• The table usually contains 5-digit number
arranged in rows and columns.
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7. • Note down number one by one from random
number table, till reach the desired Sample size.
• Using this functions we compute random number
in Excel.
=RAND() and
=RANDBETWEEN(bottom,top) 8

8. SRSWR and SRSWOR
1. Simple Random Sampling With Replacement
(SRSWR) :
• In SRSWR the units selected in the earlier draws are
replaced to the population before the next draws are
made.
• Thus a unit has a chance of being included in the
sample for more than once.
• Number of possible SRSWR sample of size 'n' from
population of size 'N' is, Nn
.
• Probability of realization of a sample ‘s’ from sample
space is
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9. 2. Sample Random Sampling Without Replacement
(SRSWOR) :
• In SRSWOR the units selected in the earlier draws
aren't replaced to the population before the next drawn
are made.
• Thus a unit has only one chance of being included in
the sample.
• Number of possible SRSWOR Sample of size 'n' from
population of size 'N' is,
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10. • Probability of realization of selecting a sample
‘s’ from sample space is
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11. Pir
(Probailiy of ith
unit to be
selected at rth
draw)
• Population size N
• Sample size n
1. Pir
for SRSWR :-
Probability of selecting each sample unit is same
• So,in SRSWR it is easy to show that Probability
of selection ith
unit at rth
draw is
1 2 … r … n-1 n
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12. 2. Pir
for SRSWOR :-
probability of selecting ith
unit at rth
draw
• => Pir
=
• => Pir
=
1 2 … r-1 r
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