continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = ½ a) Show that the area under the curve is equal to 1 b) Find P(2 < x < 2.25) c) Find P(x < 1.6)
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- Suppose you have two independent random variables X ~ Y ~ Exponential(A2), A1 > 0, d2 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P( > 1). (c) P(X +Y > 1).The number of minutes that train is early or late can be modeled by a random variable whose density is given by: g(t) = {(1/972)(81 − t^2), −9 ≤ t ≤ 9, 0 elsewhere, where negative values indicate the train arriving early and positive values indicate the train arriving late. a. Find the probability that one of the train trips will arrive more than 5 minutes early. b. Find the probability that one of the train trips will arrive between 1 and 8 minutes late. c. Without integration, give the expected number of minutes early/late. Examination of the graph and recollection of properties of integrals will allow this.The continuous random variables X and Y are statistically independent and have marginal density functions fx(x) = 2x, 0 1. y2' Calculate the probability P(X < 0.5, Y < 2)
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A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON