Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 . A factory makes lamps . The probability that a lamp is defective is 0.03 . The factory tests a random sample of 15 lamps . Let X be the number of defective lamps in the sample .
( a ) Find E ( X ) .
( b ) Find Var ( X ) .
Another random variable Y is defined such that E ( Y) �� 1.2 and Var ( Y) � 0.8 . It is given that X and Y are independent .
( c ) Find E ( �X
� Y) .
( d ) Find Var ( �X
� Y) .
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4 . A box contains four yellow balls and one purple ball . Chester plays a game by randomly drawing a ball one by one from the box , without replacement . The game ends when a purple ball is being drawn .
Chester gets $ 20 and $ 10 if he draws the purple ball in his first trial and second trial respectively . He gets nothing if he draws the purple ball after the second trial . Let X be the amount of payoff to Chester .
( a ) ( i ) Write down P ( X � 20 ).
( ii ) Find P ( X � 0 ) .
( iii ) Hence , find E ( X ) .
[ 5 ] Another random variable Y is defined such that E ( X �6 Y) � 8 . It is given that X and Y are independent .
( b ) Find E ( Y ) . [ 2 ]
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