Consider a random variable X which, for a given k > 0, has the PDFA |x|(1+x²)kfx (x) =(a) For what values of k and A is fx a valid PDF.(b) Indicate whether the expectation value E(X") for n = 1,2,3... is finite, infinite or does notexist.

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Answered: Consider a random variable X which, for…

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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(Revision.) Let X = Wo.5 + 0.5W1 – 2W2 – W3, where (W1, t > 0) is standard BM. Find the expectation E(X²).
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A random variable X is distributed according to pdf fx(x) given below fx (x) 1 -K K a) Find the value of K. b) Determine P(X > 1/2) c) Determine P(X > 0]x 1/2) ? e) What is the conditional expectation E{X | x > 1/2} ?

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Consider a random variable X which, for a given k > 0, has the PDF A |x| (1 + x²)k fx(x) = (a) For what values of k and A is fx a valid PDF. (b) Indicate whether the expectation value E(X) for n = 1, 2, 3... is finite, infinite or does not exist.