1. (Based on Book problem 2.5.8) The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Y measures the acidity of the solution. They have a joint probability density function f(x, y) = 1 625 (40-2r4y), for 0≤x≤5 and 0 ≤ y ≤5; and f(x,y) = 0 elsewhere. (a) Construct the marginal probability density functions fx(r) and fy (y). (b) Are the ethanol concentration and the acidity independent? (c) What are the expectation and the variance of the acidity Y? (d) Find E[X³].
1. (Based on Book problem 2.5.8) The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Y measures the acidity of the solution. They have a joint probability density function f(x, y) = 1 625 (40-2r4y), for 0≤x≤5 and 0 ≤ y ≤5; and f(x,y) = 0 elsewhere. (a) Construct the marginal probability density functions fx(r) and fy (y). (b) Are the ethanol concentration and the acidity independent? (c) What are the expectation and the variance of the acidity Y? (d) Find E[X³].
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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![1. (Based on Book problem 2.5.8) The random variable X measures the concentration of ethanol
in a chemical solution, and the random variable Y measures the acidity of the solution. They
have a joint probability density function
1
f(x, y) = (40-2r4y), for 0≤x≤5 and 0 ≤ y ≤5; and f(x, y) = 0 elsewhere.
625
(a) Construct the marginal probability density functions fx(x) and fy(y).
(b) Are the ethanol concentration and the acidity independent?
(c) What are the expectation and the variance of the acidity Y?
(d) Find E[X³].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0a58ad-57fb-4927-ac11-40e4d0cfe182%2F040915c9-7cbf-44bb-accd-bd2e4e1ca2cd%2Fu99xvbr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (Based on Book problem 2.5.8) The random variable X measures the concentration of ethanol
in a chemical solution, and the random variable Y measures the acidity of the solution. They
have a joint probability density function
1
f(x, y) = (40-2r4y), for 0≤x≤5 and 0 ≤ y ≤5; and f(x, y) = 0 elsewhere.
625
(a) Construct the marginal probability density functions fx(x) and fy(y).
(b) Are the ethanol concentration and the acidity independent?
(c) What are the expectation and the variance of the acidity Y?
(d) Find E[X³].
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