MATH 425 Final: Final Exam Solution
Document Summary
Math/stats 425 (instructor: edward ionides: 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. Solution: fx (x) = p(x x) = 1 (1 x)2 = 2x x2 for 0 x 1. (ii) find the probability density function of x. Solution: fx (x) = d dx fx (x) = 2(1 x) for 0 x 1. (iii) find the expected value of x. 0 xfx (x) dx = (cid:2)x2 2x3/3(cid:3)1: one evening, fyodor decides to play 10 games of roulette, betting on black each time. 0 = 1/3. (this bet wins with probability 18. 38 , and otherwise loses ). (i) find the expected value and standard deviation of his total winnings. You should write an expression which is suitable for evaluation, but you are not asked to evaluate it.
