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hw07 - (iii(4 pts Verify that the two algebraic expressions...

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ENEE 324 ASSIGNMENT 7 Due Tue 09/29 A point on the unit square [0 , 1] 2 is chosen at random according to a uniform probability assignment, i.e., the probability that it lies in a certain region (within the unit square) equals the area of that region. Let R be the distance of that random point from the origin (0 , 0). (i) (3 pts.) For every r in [0 , 1], determine P [ R r ]. (ii) (8 pts.) For every r (1 , 2], determine P [ R r ]. The answer involves an inverse cosine and requires no integration.
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Unformatted text preview: (iii) (4 pts.) Verify that the two algebraic expressions obtained in parts (i) and (ii) agree at r = 1, and that the same is true about their first derivatives. Also, confirm that the result of (ii) is correct for r = √ 2. (iv) (2 pts.) Using MATLAB or any other graphing tool, generate and submit a plot of P [ R ≤ r ] against r , for r ∈ [0 , √ 2]. (v) (3 pts.) Determine P [0 . 8 < R ≤ 1 . 2]....
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