Definition: Consider an i.i.d. random sample X1, . . . , Xn, where each Xi has p.d.f./p.m.f. f (x). Further, suppose that θ is some unknown parameter from Xi. The likelihood function is L(θ) ≡ n f (xi). i=1 Definition: The maximum likelihood estimator (MLE) of θ is the value of θ that maximizes L(θ). The MLE is a function of the Xi’s and is therefore a RV. 2 7.31 MLE’s and MOM Easy Examples iid Example: Suppose X1, . . . , Xn ∼ Exp(λ). MLE for λ. L(λ) = n i=1 f (xi) = n
Words: 1759 - Pages: 8
Trigonometric Functions of any Angle When evaluating any angle θ , in standard position, whose terminal side is given by the coordinates (x,y), a reference angle is always used. Notice how a right triangle has been created. This will allow us to evaluate the six trigonometric functions of any angle. Notice the side opposite the angle θ has a length of the y value of the given coordinates. The adjacent side has a length of the x value of the coordinates. The length of the hypotenuse is given
Words: 1220 - Pages: 5
urine suggesting that JH’s condition is progressing to renal failure. 3. What additional physical or laboratory findings would be helpful in determining JH’s degree of renal impairment? Creatinine clearance is helpful in determining general kidney function. A level above 1.2 is reduced and indicates renal impairment. The kidneys' ability to handle creatinine is called the creatinine clearance rate, which helps to estimate the glomerular filtration rate (GFR). This rate will give a general overview
Words: 387 - Pages: 2
Analysis II Solutions: June 2010 April 2013 Question 1. a) (i) (ii) The sequence an converges to a if for any 1 1 > 0 there exists an N such that |xn − a| < for n ≥ N (3n + 22n ) n = (3n + 4n ) n → max {3, 4} = 4 by a standard result. 4n2 2n +2n3 4n 8n4 2n +n3 4n = 1 4 ( n )( 1 )n +2 2 8n( 1 )n +1 2 1 4 → 2 by the product, sum and quotient rule. 1 1 4 1 1 1 1 1 1 5 5 (iii) (5n3 +6n4 ) n = 6 n n n ( 6n +1) n and limn→∞ 6 n n n = limn→∞ 6 n (n n ×n n ×n n ×n n ) = 1 and limn→∞
Words: 2948 - Pages: 12
CAUSES OF FAILURES OF SOME PUPILS IN PUBLIC ELEMENTARY SCHOOLS IN PANIQUI SOUTH DISTRICT, PANIQUI, TARLAC _________________________ A Project Paper Presented for the Completion of MAT – English ___________________________ LIBERTY G. PINGUL 2012 Table of Contents Title Page Chapter I: Introduction
Words: 3310 - Pages: 14
Homework #9 These will take some thought….FML From Chapter 16: PROBLEM 1 Thirty samples of size 4 of the customer waiting time at a call center for a health insurance company resulted in an overall mean of 10.4 minutes and average range of 0.9 minutes. Compute control limits for - and R-charts using formulas 16.3. For the R-chart: UCL = D4= 2.282*.9=2.0538 LCL = D3=0*.9=0 For the chart: UCL = + A2 = 10.4+.729(.9) = 11.0534 =11.05
Words: 342 - Pages: 2
BIO 182 LAB SIGN OFF PAGE — LESSON 13 Name _______________________________ Please staple all of your lab pages for this Lesson together with this page as the top. You will use this page to get your Labs for Lesson 13 signed off by the Biology Learning Center staff. You need to have all of the following steps initialed by a staff member before you can receive your 15 labs points for Lesson 13 and be allowed to take Exam 7. After you have obtained all of your sign offs for this Lesson, be sure that
Words: 3068 - Pages: 13
2. Graph points = Function 1: Quadrant I Quadrant IV Quadrant II Quadrant III X-Intercept (.5 or ½, 0) Y-intercept (0,-1) X, exact | X, approximate | F(x) | | 0 | 0. | -1 | Y intercept | .5 or 1/2 | .5 | 0 | X intercept | • Function 2: X-Intercept ( 6.66667 or 20/3, 0) Y-intercept (0,5) Quadrant II Quadrant I Quadrant III Quadrant IV X, exact | F(x) | | 20/3 or 6.6666666666667 | 0 | X intercept | 0 | 5 | Y intercept | • Function 3: Table 3 Q2 Q1 VERTEX
Words: 255 - Pages: 2
HSC 4555 Spring 2015 Unit 4 Case Study A 45-year old man presented to the hospital with alcohol withdrawal. After drinking a pint of brandy daily for the past 5-6 years, he decided to stop drinking 4 days ago. he experienced tremors and then visual and auditory hallucinations. On arrival at the hospital, he was diaphoretic and tachycardiac, with a pulse rate of 102. His chemistry results are shown below: Na+ | 130 mmol/L | K+ | 3.7 mmol/L | Cl- | 90 mmol/L | CO2 | 20 mmol/L
Words: 680 - Pages: 3
FILE ORGANIZATION INTRODUCTION: Before going into file organization it is necessary to go into little details of files generally. A file is a collection of related information defined by its creator. File is the basic unit of storage that enables a computer to distinguish one set of information from another. The most important files are program and data files. Program files are associated with providing access and execution of an actual program that is stored and installed on your computer system
Words: 1861 - Pages: 8
