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Binomial Distribution
Binomial Experiment -


 !
"!"#!$"
%!&
'()*

 )*
+
"+,-$"
%!&
Notation
!"


#"$
."$/0+#
Binomial Distribution
$"
$
#"1!%!#22340+3+

2
2
2"
12
5$25//
Problems
0
6'778"!60,"!
"9":
Ans -

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;
#1<;22340+3+

2
2
2"
#=>292#=29?#=2-?#=2@?#=27?#=2*?#=20?#=2,
20,94,773940+,773@?0,-4,773-40+,773-?0,@4,773@40+,7739?0,74,773740+,77
3A?0,*4,773*40+,773B?0,04,773040+,773C?0,,4,773,40+,7730,
2,CB*
2)
Ans -

#=272C74,-03740+,-039
2,0-@*7

#=D720+#=>2720+,*7@92,A9-@

#=D272#=D7?#=272,C0C9

#=>272#=27?#=2*?#=20?#=2,
2C74,-03740+,-039?C*4,-03*40+,-03A?C04,-03040+,-03B?C,4,-03,40+,-03C
2,*7@9

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Binomial Distribution Binomial Experiment-Abinomial experiment(also known as aBernoulli trial) is astatistical experimentthat has the following properties:The experiment consists ofnrepeated trials.Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.The probability of success, denoted byP, is the same on every trial.The trials areindependent; that is, the outcome on one trial does not affect the outcome on other trials.Consider the following statistical experiment. You flip a coin 2 times and count the number of times the coin lands on heads. This is a binomial experiment because:The experiment consists of repeated trials. We flip a coin 2 times.Each trial can result in just two possible outcomes - heads or tails.The probability of success is constant - 0.5 on every trial.The trials are independent; that is, getting heads on one trial does not affect whether we get heads on other trials.NotationThe following notation is helpful, when we talk about binomial probability.k: The number of successes that result from the binomial experiment.n: The number of trials in the binomial experiment.P: The probability of success on an individual trial.Q: The probability of failure on an individual trial. (This is equal to 1 -P)Binomial DistributionAbinomial random variableis the number of successesxinnrepeated trials of a binomial experiment. Theprobability distributionof a binomial ran ...
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