MATH 425 Final: Final Exam
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Electronic devices brought into the room should remain in a closed bag on the oor, and penalties will be applied if this rule is violated. For example, no cell phone usage for the duration of the exam, please! 1: let x be a continuous random variable, with. P (x > x) = (1 x)2, 0 x 1. (i) find the cumulative distribution function of x. (ii) find the probability density function of x. (iii) find the expected value of x. 2: one evening, fyodor decides to play 10 games of roulette, betting on black each time (this bet wins with probability 18. 38 , and otherwise loses ). (i) find the expected value and standard deviation of his total winnings. 3: anne and bin both plan to take the 16. 10 train to chicago. Anne"s arrival at the train station is uniformly distributed between 0 and 20 minutes before the train departs.
