Exercise 63
1 . The random variable X follows a Poisson distribution with mean b . It is given that 3 P ( X � 0 ) � P ( X � 3 ) . 32
( a ) Find b .
( b ) Hence , write down the values of
( i ) P ( X � 2 );
[ 3 ]
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( ii ) the variance of X . [ 2 ]
2 . The random variable X follows a Poisson distribution with mean c . It is given that 9P ( X �1 ) � 2P ( X � 2 ) .
( a ) Find c .
( b ) Hence , write down the values of
[ 3 ]
( i ) P ( X � 4 ) ;
( ii ) the standard deviation of X . [ 2 ]
3 . The number of digital cameras sold in a store each week follows a Poisson distribution with mean � , where � � 12 , � � . The probability that 13 digital cameras are sold in a particular week is 0.0956 .
( a ) Find � .
( b ) Hence , find the probability that more than 3 digital cameras are sold on a particular day .
[ 3 ]
[ 2 ] www . seprodstore . com
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