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Practice midterm – 1,
Time: 80 minutes
Closed book, 1 letter sized page notes
Q1.
One of two wheels of fortune, A and B, is selected by the flip of a fair coin, and the
wheel chosen is spun once to determine the experimental value of random variable X.
Random variable Y, the reading obtained with wheel A, and random variable W, the
reading obtained with wheel B, are described by the PDFs
If we are told the experimental value of X was less than 1/4 , what is the conditional
probability that wheel A was the one selected?
Q2.
A 303 graduate opens a new casino in Las Vegas and decides to make the games
more challenging from a probabilistic point of view. In a new version of roulette, each
contestant spins the following kind of roulette wheel. The wheel has radius r and its
perimeter is divided into 20 intervals, alternating red and black. The red intervals (along
the perimeter) are twice the width of the black intervals (also along the perimeter). The
red intervals all have the same length and the black intervals all have the same length.
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 Spring '08
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