Solutions to Homework #8
(W4150 Intro to Probability and Statistics, S04) Sec. 9.7. (4) n = 30; X = 780; = 40; z/2 = z0.02 = 2.054 Hence by applying formula for CI from p.235 we obtain: 40 40 ) or 765 < < 795 ) < < 780 + (2.05)( 780 (2.05)( 30 30
Sec.9.7.
(W4150 Intro to Probability and Statistics, S04) Sec. 4.1. (1) In this problem we have to integrate joint distribution density function multiplied by x with respect to both x and y - but one should be very careful when setting limits for integration. You
(W4150 Intro to Probability and Statistics, S04) Sec. 2.5. (8) Let A = cfw_there is a defect in braking system and B = cfw_there is a defect in fueling system. We are given that P(A) = .25, P(B) = .17 and P(A B) = .15. Then: (a) P(A B) = P(A) + P(B) - P(A
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4. Mathematical Expectation
4.1 Expected Value
When summarizing and describing crucial features of a
probabili
MIDTERM EXAM
A
SIEO W4150 - Introduction to Probability and Statistics
March 8, 2011
Irene Hueter
NAME
EMAIL
Show EACH of your steps in finding the solution to get credit. Each of the problems
1 through 6 carries the same number of points (Total: 100 poin
Stat 317/253
Winter 2013
HW #4 January 16
Due Wednesday January 23th, in class (at the beginning of the lecture period)
Readings: [IPM10e] Section 4.4, p.214-230 (skip Example 4.26 on p.225-228)
Problems to Turn In:
1.
[IPM10e] Exercise 4.15
2. (This prob
Syllabus for IEOR W4150 (Introduction to Probability and Statistics) Fall 2016
Course objectives This MS course is a first foray into the world of probability and statistics. At the end of this
course, you will have a basic toolkit for analyzing and under
The Gamma Function
May 16, 2000
One of the most important functions in mathematical analysis is the gamma function.
It is sometimes called the factorial function because it gives us a real analytic function
with which to compute factorials. Recall from el
Table of Contents
Table of Contents
Chapter 1: Introduction to Django . 6
What Is a Web Framework? . 6
The MVC Design Pattern . 7
Djangos History. 8
How to Read This Book . 9
MIDTERM EXAM
SIEO W4150 - Introduction to Probability and Statistics
March 7, 2016
Irene Hueter
NAME
EMAIL
Show EACH of your steps in finding the solution to get credit. Each of the problems
1 through 6 carries the same numb
STAT 4150
Introduction to
Probability & Statistics
Mondays & Wednesdays @ 7:40pm, 417 IAB
Irene Hueter, Ph.D.
Columbia University, Statistics Dept
[email protected]
About This Course
Why study probability and
statistics?
The Great Climate
1
Linear Regression
Suppose that (xi , yi ) i = 1, . . . , n denote the height in inches of adult male students and their fathers. If we plot (xi , yi ) i = 1, . . . , n we would see a linear pattern with taller fathers having taller sons. This linear pat
(W4150 Intro to Probability and Statistics, S04) Sec. 5.3. (4) (a) P(X=2) = C52(3/4)2(1/4)3 = .0879 ; or you can use tables/Excel to find the same value by taking difference P(X=2) = P(X<2) P(X<1) = 20 b(x ;5,.75) - 10 b(x ;5,.75) (b) P(X<3) = 30 b(x ;5,.
(W4150 Intro to Probability and Statistics, S04) Sec. 6.4. (1) Use tables or built-in Excel function for normal distribution to answer each question here: (a) (b) (c) (d) (e) (f) Area = (1.43) = .9236 Area = 1 - (-.89) = .8133 Area = (-.65) - (-2.16) = .2
(W4150 Intro to Probability and Statistics, S04) Sec. 9.11. (1) (a) n = 200, p = 114 / 200 = .57, q = .43, z / 2 = z 0.02 = 2.05 Hence using the formula on p.258 we obtain the interval of the form: .57 2.05 (.57)(.43) / 200 < p < .57 + 2.05 (.57)(.43) / 2
(W4150 Intro to Probability and Statistics, S04) Sec. 10.4. (1) (a) (b) Sec.10.4. (2) (a) The training is effective (b) The training is effective Sec. 10.4. (3) (a) The firm is not guilty. (b) The firm is guilty. Sec.10.4 (6) (a) = Pcfw_to reject Ho when
(W4150 Intro to Probability and Statistics, S04) Sec. 10.12. (1) H 0 : p = .4 H1 : p > . 4 = .05 If we denote the number of those who choose lasagne by X then under H0 X ~ binomial(20;.4) and so P-value is given by P[X > 9 | p = .4] = 1 P[X < 8 | p = .4]
1
1.1
1.1.1
Introduction
Syllabus
Level of the course:
The course is given at an intermediate level. The course requires one year of calculus and a certain degree of mathematical maturity. This is an ambitious course in that we cover both probability and
1
Lecture Plan
Experiments, Outcomes and Events The Axioms of Probability Axiom consequences Finite Sample Space.
2
Experiments, Outcomes, Sample Space, and Events
Experiment: Toss a coin three times. Outcomes: The possible outcomes are hhh, hht, hth, h
1
Lecture Plan
Finite Sample Space (Review). Conditional Probability Independence Random Variables Expected Values Markovs Inequality
2
Finite Sample Space (Review)
S = cfw_w1 , w2 , . . . , wN and let pi = P (cfw_wi ), i = 1, . . . , N. By axiom A1 we