(a) For fx(x) = 1-x| |x|≤1 " otherwise sketch the PDF, then calculate E[X] and P[|X| > 1/2].
(a) For fx(x) = 1-x| |x|≤1 " otherwise sketch the PDF, then calculate E[X] and P[|X| > 1/2].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
Related questions
Question
Calculate each of the requested quantities. All of these problems are carefully chosen so that they can be completed without
![(a) For fx (x):
=
{}
1−|x| |x|≤1
otherwise'
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 Y
well 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 a
such that P[X ≤ a] ≤ 0.1. Determine the minimum value of b such that P[X ≥ b] ≤ 0.2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02681530-b6ca-4d72-bfd1-7260256101ab%2F50be216d-560d-4472-9d89-8d500816b469%2F6h9vmsr_processed.png&w=3840&q=75)
Transcribed Image Text:(a) For fx (x):
=
{}
1−|x| |x|≤1
otherwise'
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 Y
well 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 a
such that P[X ≤ a] ≤ 0.1. Determine the minimum value of b such that P[X ≥ b] ≤ 0.2.
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