Calculate each of the requested quantities. All of these problems are carefully chosen so that they can be completed without integration, so we are expecting exact answers. For the Gaussian problems, you will sometimes need to lookup values for the standard normal CDF Φ(z). (a) For fx (x):={}1−|x| |x|≤1otherwise'sketch the PDF, then calculate E[X] and P[|X| > 1/2].(b) For fx(x) from part (a), determine and sketch the conditional PDF fx|Â(x) given the event{|X| > 1/2}. Using your sketch, calculate P[X > 0||X|>1/2].(c) Let X be Exponential (2). Calculate E[X – 1] and E[(X − 1)²].(d) Let X be Uniform(-2, 3). Determine P[X – 1 > 0] and P[X² – 1 > 0].(e) Let X be Gaussian (2, 1) and let Ywell as P[Y > 1].= 3X 2. Determine the mean and variance of Y as(f) Let X be Gaussian (1,4). Determine (up to two decimal places) the maximum value of asuch that P[X ≤ a] ≤ 0.1. Determine the minimum value of b such that P[X ≥ b] ≤ 0.2.

(a)"As per the Bartleby guidelines, we can solve only one question at a time.The probability density…

Answered: (a) For fx(x) = 1-x| |x|≤1 " otherwise…

Math

Statistics

(a) For fx(x) = 1-x| |x|≤1 " otherwise sketch the PDF, then calculate E[X] and P[|X| > 1/2].

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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