Probability Distributions, Continuous Variables
Objectives: (Chapter 6, DeCoursey)
- To establish the difference between probability distribution for discrete and continuous variables. - To learn how
Probability Distributions, Discrete Random Variables
Objectives: (Chapter 5, DeCoursey)
- To define a probability function, cumulative p probability, p y probability distribution function y and cumula
Regression and Correlation of Data
- Apply the least squares method for fitting data with linear regression - Methods of regression are used to summarize sets of data in useful form. The values of the
One way One-way Analysis of Variance
ANOVA Analysis of Variance is used with quantitative and qualitative data to find whether each input has significant effect on the system's response.
Estimates o
Normal Distribution
Objectives: (Chapter 7, DeCoursey)
- To define the Normal distribution, its shape, and its probability function p y - To define the variable Z, which represents the number of stand
Note 7
Statistical Inference for the Mean: t-test
When variance is estimated from a sample, t-distribution applies. T-Distribution: a distribution related to normal distribution but taking into accoun
Statistical Inference for the Mean: t-test
Comparison of sample means using unpaired samples: - We have samples for each of two conditions. We provide an answer for "Are the two sample means significa
Statistical Inference for the Mean: t-test
Comparison of paired samples: - Interfering factors in the comparison of two sample means using unpaired samples may inflate the pooled estimate of variance
Statistical Inferences for Variance
Objectives:
Learn to compare variance of a sample with variance of a population Learn to compare variance of a sample with variance of another sample Introduce chi
Regression and Correlation of Data
Other forms with single input or regressor:
1 = a + bx y
ln y = a + bx
y = a + bx 3
f1( y) = a + b f2 (x)
Method: 1. Convert the equation to simple linear form by se
Solutions to Homework Assignment #2
Math 5652 (Stochastic Processes), Spring 2017
First, the solutions to the problems from the book:
1.9. (a) If we write = (x, y, z) we need to solve the equation
0.
Quiz 1: Solutions
October 18, 2016
The Basic Solow Model
a.) Derive the per capita production function.
Y = K L1
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L L1
K L1
L L1
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Recall
Regression and Correlation of Data
Objective:
Fit a polynomial with the Least Squares Method
Regression and Correlation of Data
Fitting the polynomial with the least squares approach
Pn ( x) = a 0 +
Normal Distribution
Objectives: (Chapter 7, DeCoursey)
- To define the Normal distribution, its shape, and its probability function p y - To define the variable Z, which represents the number of stand
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Basic Probability
(Chapter 2, W.J.Decoursey, 2003)
Basic Probability
Probability:
A measure of the likelihood that a particular event will occur. e.g. If we are certain that an event will occur, its p
Basic Probability
Permutations and Combinations:
- Combinations:
- The number of different packages of data taken r at time from a data set containing n items The order of items is items. inconsequent
Confidence level: An alternative representation of level of significance. - normal distribution applies applies. - level of significance (e.g. 5% in two tails) determines the rejection region, which m
Regression and Correlation of Data
Correlation: Correlation is a measure of the association between random variables, say X and Y. No assumption that one of these variables is known without error. Ass
Descriptive Statistics
Objectives: (Chapter 3, Decoursey)
- To understand the definition of , median, variance, standard deviation, mean absolute deviation and coefficient variation and calculate thes
To calculate the number of combinations for n distinguishable items: Three laboratories to be cleaned: Biosorption, Pilot Plant and Fermentation. How many different combinations of cleaning the three
Introduction to Design of Experiments
Professional engineers are very frequently responsible for devising d i i experiments t answer practical problems. Th i t to ti l bl There are well-tried methods
Solutions to Homework Assignment #1
Math 5652 (Stochastic Processes), Spring 2017
First, the solutions to the review problems:
1. First we observe that
P (A B) = P (A) P (A B c ) = 0.6 0.4 = 0.2.
Then