Y - amount we need to pay
P(X=0)=P(Y=0)=e-0.6=0.5488
P(X=1)=P(Y=1000)=0.6e-0.6=0.3293
P(X≥2)=P(Y=2000)=1-1.6e-0.6=0.1219
EY=0*0.5488+1000*0.3293+2000*0.1219=573.1
EY2=02*0.5488+10002*0.3293+20002*0.1219=816900
VarY=EY2-(EY)2=816900-573.12=488456
SD="\\sqrt{488456}" =699
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Suppose that an airline accepted 12 reservations for a commuter plane with 10 seats. They know that 7 reservations went to regular commuters who will show up for sure. The other 5 passengers will show up with a 50% chance, independently of each other. Find the probability that the flight will be overbooked.
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