Your Practice Set – Applications and Interpretation for IBDP Mathematics
63
Paper 1 – Mean and Variance
Example
The random variable X follows a Poisson distribution with mean a . It is given that 24.5P ( X � 0 ) � P ( X � 2 ) .
( a ) Find a .
( b ) Hence , write down the values of
[ 3 ]
( i ) P ( X � 3 ) ;
( ii ) the variance of X . [ 2 ]
Solution
( a ) 24.5P ( X � 0 ) � P ( X � 2 )
�a
�e �a � e �a
�24.5�
�� � 0 ! � 2 !
24.5e
2 a �
�a
2 �a ae
0 �a
2
( M1 ) for setting equation
� ( A1 ) for correct approach 2
49 a �� 7 ( Rejected ) or a � 7
A1
( b ) ( i ) P ( X �3 ) � 0.0521292524 P ( X �3 ) � 0.0521
A1
[ 3 ]
( ii ) 7 A1 [ 2 ]
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