Your Practice Set – Applications and Interpretation for IBDP Mathematics

Paper 1 – Problems Involving Poisson Distribution

Example

Two independent random variables X and Y are distributed such that X ~ Po ( 9 ) and Y ~ Po ( 7 ) . Find

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Solution

( a ) E ( X �Y) � E ( X ) � E ( Y)

E ( X �Y) � 9� 7

( A1 ) for substitution

E ( X �Y) � 16

A1

( b ) P ( X �Y �16 ) �1� P ( X �Y

� 16 ) ( M1 ) for valid approach

( c )

P ( X �Y

�16 ) �1�

0.5659624252

P ( X �Y

�16 ) � 0.4340375748

P ( X �Y

�16 ) � 0.434 A1

2 2

Var ( 3X � 2 Y) � 3 Var ( X ) � 2 Var ( Y)

Var ( 3X

� 2 Y) � 9 ( 9 ) � 4 ( 7 ) ( A1 ) for substitution

Var ( 3X

�2 Y) � 109 A1

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