we are given independent random variables X and Y distrubuted: X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5. Show that the expression for the log-likehood function is given by: l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ. make a sketch of l(θ) for θ ∈ [0, 10]. for which value of θ does l(θ) reach its maximum?

we are given independent random variables X and Y distrubuted: X ∼ poisson(θ) , Y ∼ poisson(2θ), and observations x = 3 and y = 5. Show that the expression for the log-likehood function is given by: l(θ)=[5ln(2)−ln(3!)−ln(5!)]+8lnθ−3θ. make a sketch of l(θ) for θ ∈ [0, 10]. for which value of θ does l(θ) reach its maximum?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

How was the correct answer of 12.5000 and 2.0833 attained?
Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)
Question 1 1. Suppose you are given that a continuous random variable has a moment generating function of M (t) = 1-3.21 Find the mean and variance of the random variable. mean = var =
Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1
Question 9 Let X be an Exponential random variable, with the moment generating function (MGF): M(t) = (1-0)-¹. (a) Derive the MGF above. (b) Derive E(X) using the MGF. (c) Derive V(X) using the MGF. (d) Find the MGF of Y, where Y = 2X - 3.
Question 1 1. Suppose you are given that a continuous random variable has a moment generating function of 1 M (t) = 1-3.2t Find the mean and variance of the random variable. mean = var =
Solve it early I upvote
Question 1: Let X beta(a, 1). Find the distribution of- log(X). Hint: Use the fact that I'(a+1) = al(@)
Compute E(310) for the following model, where & wn(0, 0.16), i.e., a white noise process with mean zero and variance 0.16. Please give the exact answer. 1 Me=Mt-2+ Ct, 30 = 1.
Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?
Suppose the random variable X has the following PDF: 2 √2π This distribution is often called half-normal. Find E(X) and V(X). f(x) = , for x > 0.
2.11 Let X have the standard normal pdf, fx(x) = (1/√√2π) e¯2²/² (a) Find EX² directly, and then by using the pdf of Y = X2 from Example 2.1.7 and calculating EY. (b) Find the pdf of Y = |X|, and find its mean and variance.