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expression a (b) Consider the sequence of functions ,(r) = |r|" for n e N. Sketch functions, i.e. sketch 1(r) |r, 2(x) = |r|2 and o3(r) |r3 given by r E [-1, 1] showing all three functions in one coordinate sure your sketch shows clearly what happens at r E {-1,0, 1}. (c) Consider the sequence of random variables Y, part (b). Compute the pdf fy,. P.(X) with o, (d) Show that lim, P(Y >y) = 0 holds for any y> 0. Also compu 0). [TYPE:] Discuss carefully whether the two findings contradict

expression a (b) Consider the sequence of functions ,(r) = |r|" for n e N. Sketch functions, i.e. sketch 1(r) |r, 2(x) = |r|2 and o3(r) |r3 given by r E [-1, 1] showing all three functions in one coordinate sure your sketch shows clearly what happens at r E {-1,0, 1}. (c) Consider the sequence of random variables Y, part (b). Compute the pdf fy,. P.(X) with o, (d) Show that lim, P(Y >y) = 0 holds for any y> 0. Also compu 0). [TYPE:] Discuss carefully whether the two findings contradict

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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part C and D

2. Let X follow the distribution with pdf given via the expression { | THE -1 <x < 1 otherwise fx(x) = 1+|z| (a) Find the constant C > 0 that makes the above expression a valid pdf. (b) Consider the sequence of functions on (x) = |æ|" for n eN. Sketch the first three functions, i.e. sketch o1(x) = |r|, 2(x) = |r|2 and o3(x) = |r3 on the domain given by r e [-1, 1] showing all three functions in one coordinate frame. Make sure your sketch shows clearly what happens at r E {-1,0, 1}. (c) Consider the sequence of random variables Y, = ¢n(X) with o, defined as in part (b). Compute the pdf fy,. (d) Show that lim,n+ P(Yn > y) = 0 holds for any y > 0. Also compute lim, P(Yn < 0). [TYPE:] Discuss carefully whether the two findings contradict each other.
Transcribed Image Text:2. Let X follow the distribution with pdf given via the expression { | THE -1 <x < 1 otherwise fx(x) = 1+|z| (a) Find the constant C > 0 that makes the above expression a valid pdf. (b) Consider the sequence of functions on (x) = |æ|" for n eN. Sketch the first three functions, i.e. sketch o1(x) = |r|, 2(x) = |r|2 and o3(x) = |r3 on the domain given by r e [-1, 1] showing all three functions in one coordinate frame. Make sure your sketch shows clearly what happens at r E {-1,0, 1}. (c) Consider the sequence of random variables Y, = ¢n(X) with o, defined as in part (b). Compute the pdf fy,. (d) Show that lim,n+ P(Yn > y) = 0 holds for any y > 0. Also compute lim, P(Yn < 0). [TYPE:] Discuss carefully whether the two findings contradict each other.
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