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assignment3

# assignment3 - assignment 3 1 Let X be the maximum of the...

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assignment 3 1. Let X be the maximum of the number of heads obtained when Carlos and Michael each flip a fair coin twice. (a) Describe the underlying space S of this random experiment and specify the probabilities of its elementary events. (b) Show the mapping form S to S X , the range of X . (c) Find the probabilities for the various values of X . 2. A dart is equally likely to land at any point inside a circular target of radius 2. Let R be the distance of the landing point from the origin. (a) Find the sample space S and the sample space of R , S R . (b) Show the mapping form S to S R . (c) The “bull’s eye” is the central disk in the target of radius 0.25. Find the event A in S R corresponding to “dart hits the bull’s eye.” Find the equivalent event in S and P [ A ]. (d) Find and plot cdf of R . 3. The cdf of the random variable X is given by: F X ( x ) = 0 x < 1 0 . 5 1 x 0 (1 + x ) / 2 0 x 1 1 x 1 (a) Plot the cdf and identity the type of random variable. (b) Find P [ X 2] , P [ X = 0] , P [ X < 0] , P [2 < X < 6] , P [ X > 10]. 4. The random variable X has cdf shown in the figure below. (a) What type of random variable is

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assignment3 - assignment 3 1 Let X be the maximum of the...

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