Exercise 66
1 . Two independent random variables X and Y are distributed such that X ~ Po ( 5.5 ) and Y ~ Po ( 3.5 ) . Find
( a ) E ( X � Y) ;
( b ) P ( 5 � X �Y
� 8 ) ;
( c ) Var ( X � 4 Y) .
[ 2 ] 2 . Three independent random variables W , X and Y are distributed such that W ~ Po ( 12 ) ,
X ~ Po ( 18 ) and Y ~ Po ( 4 ) . Find
[ 2 ]
[ 2 ]
15
( a ) E ( W �X � Y) ;
( b ) P ( W � X �Y
� 30 );
( c ) Var ( 3W �2 X � Y) .
[ 2 ]
3 . In a fast food shop , the number of hamburgers and onion ring boxes sold follow Poisson distributions with means 24 per hour and 15.5 per hour respectively .
( a ) Find the expected total number of hamburgers and onion ring boxes sold in a particular hour .
[ 2 ]
( b ) Find the probability that a total number of 38 hamburgers and onion ring boxes are sold in a particular hour .
[ 2 ]
( c ) Find the probability that , in six 1-hour intervals , a total number of 38 hamburgers and onion ring boxes are sold in each interval .
[ 2 ]
4 . On a website , the number of views of a football video and a basketball video follow Poisson distributions with means 195 per day and 180 per day respectively .
( a ) Find the expected total number of views of the football video and the basketball video on a particular day .
[ 2 ]
( b ) Find the probability that there are a total of 376 views of the football video and the basketball video on a particular day .
[ 2 ] ( c ) Find the probability that , in three 1-day periods , there are a total of 376 views of the football video and the basketball video on each period . [ 2 ]
[ 2 ]
[ 2 ] www . seprodstore . com
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