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

3.2.13 Y is a continuous random variable with { 2(1- y), 0< y < 1; fy(4) = { 0, otherwise. Derive Fy(t).
.1. What is the probability that an arrival to an infinite capacity 4 server Poison queueing system with λ/μ = 3 and Po = 1/10 enters the service without waiting?
EXAMPLE 6.39 If cu = 4/5 in an (M/M/c): (/FCFS) queueing system, find the average number of customers in the non-empty queue.
Suppose a sample consists of the numbers 1, 2, 3 ... 2n, the probability of choosing an integer k is proportional to log k. Show that the conditional probability of choosing the integer 2 given that an even number is chosen is Log 2/N log 2 + log (n!)
How was the correct answer of 12.5000 and 2.0833 attained?
2.5.7. Let the random variables X1 and X2 have the joint pdf f(x1,x2) = 1/T, for (x1 – 1)2 + (2 +2)2 < 1, zero elsewhere. Find fi(æ1) and f2(x2). Are X1 and X2 independent? %3D
Imagine you have two estimators X and Y, for unknown parameter µ. Assume that they are estimated from independent datasets. Let Z = }(X+Y) be the average of these two estimators. To write the symbol µ, you can write mu. For other math notation, you can E[X], Var(X) and (X+Y)/2 or (1/2)(X+Y). Part a - If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short derivation. Part bL Assume Var(X) = Var(Y). Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.
10.5 3.5 10.5 Let + [10 f(x) dx = 9, [." *F(x) dx = 2, and [... (a) [F(x f(x) dx = 4 7 (6f(x) — 5) dx = | - (b) S (6f(x) X f(x) dx = 3. Find the following.
Solve it early I upvote
The logarithm of the ratio of the output to the input current of a transistor is called its current gain. If cur-rent gain measurements made on a certain transistor are normally distributed with μ = 1.8 and σ = 0.05, find theprobability that the current gain will exceed the requiredminimum value of 6.0.
3. Let X1, and E- X; are independent. , Xn be iid with exponential distribution with mean 0. Show that (X1+X2)/ E=1 X;
Assume the lifetime of electronic systems T (based on months) has Exponential distribution with λ=0.01. We select a random sample of 5 systems (random lifetime of these systems are T1, T2, T3, T4, and T5). Assume, S= T1+T2+ T3+ T4+ T5. a. Find E[S] . b. Find Standard Deviation of S (σSσS). c. Find median of T1.