e)Mathematically, the MLE for λ, is 1̄x = 3.2634033, which we expected. Using R and optimize(), computethe maximum of the likelihood function from a computer science standpoint.f)Plot and optimize the log-likelihood function as well. Where is the location of the maximum? Please solve this with R code Next on your own you'll plot the likelihood based on exponential data.a)First, write and simplify the likelihood function for a data set of exponentially distributed random variables.Use LaTeX math typesetting notation to make your likelihood render correctly.b)Next, consider observations from an exponential distribution where X is a the parameter. Code up a functionL_Exponential, similar to the L_Poisson from class and L_Normal from problem 1, that will take an inputvector of possible λs, an input vector of observed data, and compute and output the evaluated likelihoodvalue. Be cautious with parentheses.c)Suppose we observe a data set of heavy metal concentrations, in micrograms of mercury per liter, of wa-ter specimens collected in the Olentangy River basin: c(0.51, 0.02, 0.15, 0.46, 0.11, 0.04, 0.39,0.52, 0.2, 0.17, 0.01, 0.02, 0.32, 1.37). Suppose concentrations can be assumed to be exponen-tially distributed. Compute x, the MLE for X.mercury <-c(0.51, 0.02, 0.15, 0.46, 0.11, 0.04, 0.39, 0.52, 0.2, 0.17, 0.01, 0.02, 0.32, 1.:xbar <- mean (mercury)print (xbar)## [1] 0.3064286d)Plot the likelihood function for this particular data set over the λ domain (0, 10]. Comment on the shape ofthe likelihood function and the apparent location of the maximum.

In this problem, we focus on analyzing a data set consisting of heavy metal concentrations in water…

e) Mathematically, the MLE for λ, is 1 ̄x = 3.2634033, which we expected. Using R and optimize(), compute the maximum of the likelihood function from a computer science standpoint. f) Plot and optimize the log-likelihood function as well. Where is the location of the maximum? Please solve this with R code

e) Mathematically, the MLE for λ, is 1 ̄x = 3.2634033, which we expected. Using R and optimize(), compute the maximum of the likelihood function from a computer science standpoint. f) Plot and optimize the log-likelihood function as well. Where is the location of the maximum? Please solve this with R code

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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Question

Mathematically, the MLE for λ, is 1

̄x = 3.2634033, which we expected. Using R and optimize(), compute

the maximum of the likelihood function from a computer science standpoint.

Plot and optimize the log-likelihood function as well. Where is the location of the maximum?

Please solve this with R code

Next on your own you'll plot the likelihood based on exponential data.
a)
First, write and simplify the likelihood function for a data set of exponentially distributed random variables.
Use LaTeX math typesetting notation to make your likelihood render correctly.
b)
Next, consider observations from an exponential distribution where X is a the parameter. Code up a function
L_Exponential, similar to the L_Poisson from class and L_Normal from problem 1, that will take an input
vector of possible λs, an input vector of observed data, and compute and output the evaluated likelihood
value. Be cautious with parentheses.
c)
Suppose we observe a data set of heavy metal concentrations, in micrograms of mercury per liter, of wa-
ter specimens collected in the Olentangy River basin: c(0.51, 0.02, 0.15, 0.46, 0.11, 0.04, 0.39,
0.52, 0.2, 0.17, 0.01, 0.02, 0.32, 1.37). Suppose concentrations can be assumed to be exponen-
tially distributed. Compute x, the MLE for X.
mercury <-c(0.51, 0.02, 0.15, 0.46, 0.11, 0.04, 0.39, 0.52, 0.2, 0.17, 0.01, 0.02, 0.32, 1.:
xbar <- mean (mercury)
print (xbar)
## [1] 0.3064286
d)
Plot the likelihood function for this particular data set over the λ domain (0, 10]. Comment on the shape of
the likelihood function and the apparent location of the maximum.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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