fx(x) = 1+|z| otherwise a) Find the constant C>0 that makes the above expression a valid po b) Consider the sequence of functions ,(x) = |a|" for n E N. Sketch ti functions, i.e. sketch 1(r) |r, 2(r) = |r|2 and o3(x) = |r3 on given by r E [-1, 1] showing all three functions in one coordinate f sure your sketch shows clearly what happens at r E{-1,0, 1}. c) Consider the sequence of random variables Y, := 0,(X) with o, c part (b). Compute the pdf fy,-. d) Show that lim,- P(Yn > y) = 0 holds for any y > 0. Also compute 0). [TYPE:] Discuss carefully whether the two findings contradict ea
fx(x) = 1+|z| otherwise a) Find the constant C>0 that makes the above expression a valid po b) Consider the sequence of functions ,(x) = |a|" for n E N. Sketch ti functions, i.e. sketch 1(r) |r, 2(r) = |r|2 and o3(x) = |r3 on given by r E [-1, 1] showing all three functions in one coordinate f sure your sketch shows clearly what happens at r E{-1,0, 1}. c) Consider the sequence of random variables Y, := 0,(X) with o, c part (b). Compute the pdf fy,-. d) Show that lim,- P(Yn > y) = 0 holds for any y > 0. Also compute 0). [TYPE:] Discuss carefully whether the two findings contradict ea
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a398c26-6abf-4ee8-a36f-aa14e93f068a%2Fa7edc01c-d899-42ce-9ed4-60feedcd3628%2F70nnd98_processed.jpeg&w=3840&q=75)
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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