Robin throws darts at a circular target of radius r and is equally likely to hit any point in the target (the probabilit

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Robin Throws Darts At A Circular Target Of Radius R And Is Equally Likely To Hit Any Point In The Target The Probabilit 1 (280.18 KiB) Viewed 21 times

Robin throws darts at a circular target of radius r and is equally likely to hit any point in the target (the probability that the dart hits in a given region is the area of that region divided by the area of the target). Let X be the distance of Robin's hit from the centre of the target. (a) Find the cumulative distribution function Fx(x) of X. (b) Use Fx to find the probability the dart lands in the an- nulus with radii @ and (c) Without finding the probability density function, find the expected distance from the centre, E(X). (Hint: Use the Continuous Tail Sum Formula, see Prop. 5.5 in your text- book. Make sure to verify that you can actually use this result in this situation.) (d) Find the probability density function of X. (e) If Robin's throw gets a score of S 12, compute E(S) and show it diverges. 2.