3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an observed value of a random variable X 4 U (0, 6). The random variable X divides the interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively. Denote by Y the length of the shorter of the two intervals. (a) Draw a picture which illustrates the value of Y as a function of the possible values of X. (b) Describe the support of Y and find the probability P(Y > y) for any given y. (c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of Y?

3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an observed value of a random variable X 4 U (0, 6). The random variable X divides the interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively. Denote by Y the length of the shorter of the two intervals. (a) Draw a picture which illustrates the value of Y as a function of the possible values of X. (b) Describe the support of Y and find the probability P(Y > y) for any given y. (c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of Y?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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