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Binomial Distribution
� Properties of a random variable X ~ B ( n, p ) following binomial distribution : 1 . Only two outcomes from every independent trial ( Success and failure ) 2 . n : Number of trials 3 . p : Probability of success 4 . X : Number of successes in n trials
� Formulae for binomial distribution :
1 . |
�n� r n�r
P (
X
� r)
�
�
�p
( 1
� p) for 0
�r� n, r �
�r �
|
2 . |
E (
X
)
� np
: Expected value of X
|
3 . Var ( X ) �np( 1 � p) : Variance of X
4 . np( 1 � p)
: Standard deviation of X 5 . P ( X � r) � P ( X � r �1 ) �1� P ( X � r � 1 )
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Normal Distribution
� Properties of a random variable 1 . � : Mean 2 . � : Standard deviation
2
X ~ N ( �� , ) following normal distribution :
3 . The mean , the median and the mode are the same 4 . The normal curve representing the distribution is a bell-shaped curve which is symmetric about the middle vertical line 5 . P ( X � �) � P ( X � �) � 0.5 6 . The total area under the curve is 1
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