352 Frequently Asked Questions In Quantitative Finance
Minimum and maximum correlation IfX,YandZare three
random variables such thatXandYhave a correlation
of 0.9, andYandZhave correlation of 0.8, what are
the minimum and maximum correlation thatXandZ
can have?
(Thanks to jiantao.)
Airforce One One hundred people are in line to board
Airforce One. There are exactly 100 seats on the plane.
Each passenger has a ticket. Each ticket assigns the
passenger to a specific seat. The passengers board the
aircraft one at a time. GW is the first to board the plane.
He cannot read, and does not know which seat is his,
so he picks a seat at random and pretends that it is his
proper seat.
The remaining passengers board the plane one at a
time. If one of them finds their assigned seat empty,
they will sit in it. If they find that their seat is already
taken, they will pick a seat at random. This contin-
ues until everyone has boarded the plane and taken
a seat.
What is the probability that the last person to board
the plane sits in their proper seat?
(Thanks to Wilbur.)
Hit-and-run taxi There was a hit-and-run incident involv-
ing a taxi in a city in which 85% of the taxis are green
and the remaining 15% are blue. There was a witness to
the crime who says that the hit-and-run taxi was blue.
Unfortunately this witness is only correct 80% of the
time. What is the probability that it was indeed a blue
car that hit our victim?
(Thanks to orangeman44.)
