fx(x) = 5x²(x - 1)(x-3) [0≤x≤ 1] (a) Find the location of the maximum of fx(x) for 0 ≤ x ≤ 1, and show that fx(x) < 2 for 0 ≤ x ≤ 1. (b) Sketch the density function fx(x) for 0 ≤ x ≤ 1. (c) Consider the following 10 independently generated samples from
fx(x) = 5x²(x - 1)(x-3) [0≤x≤ 1] (a) Find the location of the maximum of fx(x) for 0 ≤ x ≤ 1, and show that fx(x) < 2 for 0 ≤ x ≤ 1. (b) Sketch the density function fx(x) for 0 ≤ x ≤ 1. (c) Consider the following 10 independently generated samples from
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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Parts a), b), c) previously answered
![A continuous random variable X ~ D on [0, 1] has density function fx
given by
fx(x) = 5x? (x – 1)(x – 3) [0 <x < 1]
(a) Find the location of the maximum of fx(x) for 0 < x < 1, and
show that fx(x) < 2 for 0 < x <1.
(b) Sketch the density function fx(x) for 0 <x< 1.
(c) Consider the following 10 independently generated samples from
the rectangular distribution R = Uni((0, 1)) × Uni((0, 2)) on the
rectangle (0, 1) × (0,2).
(0.86, 0.33) (0.48, 0.56) (0.21,0.17) (0.21,0.55) (0.92, 1.57)
(0.64, 0.02) (0.30, 0.60) (0.60, 1.58) (0.52,0.40) (0.80, 1.24)
Mark these 10 samples on the sketch of the density function fx.
(d) Use these samples to generate 8 realisations of the distribution D.
(e) Estimate the mean of D using these realisations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff258f736-2efe-4abc-a546-b1bd73d984a7%2F055550f3-f74e-4013-a781-e3558a75e18a%2F7sz3ztq_processed.png&w=3840&q=75)
Transcribed Image Text:A continuous random variable X ~ D on [0, 1] has density function fx
given by
fx(x) = 5x? (x – 1)(x – 3) [0 <x < 1]
(a) Find the location of the maximum of fx(x) for 0 < x < 1, and
show that fx(x) < 2 for 0 < x <1.
(b) Sketch the density function fx(x) for 0 <x< 1.
(c) Consider the following 10 independently generated samples from
the rectangular distribution R = Uni((0, 1)) × Uni((0, 2)) on the
rectangle (0, 1) × (0,2).
(0.86, 0.33) (0.48, 0.56) (0.21,0.17) (0.21,0.55) (0.92, 1.57)
(0.64, 0.02) (0.30, 0.60) (0.60, 1.58) (0.52,0.40) (0.80, 1.24)
Mark these 10 samples on the sketch of the density function fx.
(d) Use these samples to generate 8 realisations of the distribution D.
(e) Estimate the mean of D using these realisations.
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