1. The sum of two exponential random variables: 1.1 The standard exponential random variable has R name exp and pdf f₁(x) = exp(-x). Use the command curve(dexp, 0, 5) to plot this pdf from 0 to 5. 1.2 The sum of two independent exponential random variables has pdf f₂(x) = x exp(-x). Use f2=function(x){x*exp(-x)} to define this function in R and use the curve command to plot it from 0 to 7. 1.3 Generate a 2x10,000 matrix whose entries are random numbers generated from the standard exponential distribution. a) Make a histogram of the first row and check if this matches the plot of f₁. b) Make a histogram of the sum of the first two rows and check if it matches the plot of f₂.

1. The sum of two exponential random variables: 1.1 The standard exponential random variable has R name exp and pdf f₁(x) = exp(-x). Use the command curve(dexp, 0, 5) to plot this pdf from 0 to 5. 1.2 The sum of two independent exponential random variables has pdf f₂(x) = x exp(-x). Use f2=function(x){x*exp(-x)} to define this function in R and use the curve command to plot it from 0 to 7. 1.3 Generate a 2x10,000 matrix whose entries are random numbers generated from the standard exponential distribution. a) Make a histogram of the first row and check if this matches the plot of f₁. b) Make a histogram of the sum of the first two rows and check if it matches the plot of f₂.

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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