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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