Electromagnetic radiation o Frequency (nu) number of peaks that pass a given point per time o Wavelength distance from one wave to the next Parts of a wave o Nodes where the wave crosses an axis o Trough low point in wave 1/ = R(1/m2) (1
MATH 226 October 1, 2007 Factor Study o Factor A with levels 1 through I o Factor B with levels 1 through J Ybarij if level i of factor A and level j of factor B is used Dipping 1 Spraying 2 Primer Type 1 ybar11 ybar12 = 5.3 Ybar1 = 4.78 Primer T
MATH 226 September 24, 2007 X Predictor variable Y Response variable Generalizations To polynomial equations To two or more predictors x1 = height (C2) x2 = width (C1) y = volume (C3) First Model: Volume vs. Height y-hat = b0 + b1x1 y-hat =
MATH 226 September 19, 2007 Find numerical quantities that describe whether the linear model is good or not o raw variation (yi y-bar)2 o variation after fitting the line (yi i)2 o percent of variation explained by the regression line: R2 = (yi
MATH 226 September 17, 2007 Least Squared Line given n sets of paired (x, y) data points We want to find: y-hat = 0 + 1x we minimize L = (yi yi-hat)2 = (yi 0 + 1xi )2 L/0 = -2(yi 0 + 1xi)(yi 1 1xi) L/1 = -2(yi 0 + 1xi)(yi 0 1xi) SEE BEST FI
MATH 226 September 12, 2007 Sample o X-bar = 3,000,000 o S = 2,827,948 Population o = 4,632,344 o = 4,500,267 where o s2 = (xi x-bar)2/(n-1) o 2 = (xi )2/N o = sqrt(N-1/N)*s
MATH 226 September 10, 2007 Numerical Summaries o Summary of location Sample Median 0.5 quantile; Q(.5); very center of the data range Sample Mean sum of all numbers divided by number of numbers x-bar = sigma(x, 1n)/n Sample Mode most often o
MATH 226 September 5, 2007 Definition: x1 < x2 < . < xn ordered data For p = (i )/n, I = 1, 2, 3,., n o The quantile p is defined as Q(p) o (i )/10 Q(i )/10) i 1 .05 1.0 2 .15 3.5 3 .25 8.1 4 .35 8.2 5 .45 9.0 6 .55 9.7 7 .65 9.8 8 .75 12.0 9 .
MATH 226 September 3, 2007 A simple random sample of size n is a subset of the population containing n elements and chosen in such a way that any subset of the population containing n elements is equally likely to be chosen. Stratified random samp
MATH 226 August 29, 2007 Comparative Study testing of a new method against an existing one o Paired data is preferred when collecting Example: Testing a suspension at the beginning and then retest after a certain amount Replication be sure that
MATH 226 August 27, 2007 Data Collection Numerical Non-numerical (categorical) Thickness of a stack of paper Pages 353-609 = 128 pages Total thickness = 8 cm Thickness of a single piece = 62.5 m Validity make sure that the data expresses the prop
MATH 226 October 3, 2007 Regression object to build a model, such that observations y can be predicted from x (x1, xn) Comparison of effects o (1) = 1 + 1xif 1 > 2 x has bigger influence on y (2) = 2 + 2x in model 1 than in 2 o All variables are
MATH 226 October 8, 2007 Random Variable o A real valued function of the sample space of the experiment o A real variable is discrete if the range consists of single points, and if it consists of an interval of real numbers then it is considered co
Ideal Gas Law PV = nRT (P +(a*n2)/V2)(V n*b) = nRT
Percent Composition percentage by mass = mass of part/ mass of whole
Formula Description AB Linear HAx Single H AxOH OH at 1 end Ox Ay O at 1 end Nx Ay N at 1 end NonAx All elements polar CxAy Car
MATH 226 November 19, 2007 Hypothesis tests and Confidence Intervals about the difference of means X1 and C2 are random variables Mu1 = EX1, mu2 = EX2, sigma1^2 = varX1, sigma2^2 = varX2 N1 = sample size of X1 data, Xbar1 = sample mean of X1 N2
MATH 226 November 7, 2007 Hypothesis testing o Example 34 X = blood lead concentration in black children less than 5 years old = EX H0: = 14 (g/dL) Ha: > 14 Test statistic: Z = (xbar 14)/(s/(200) ~ N(0,1) under H0 Large values of Z count a
MATH 226 November 5, 2007 Confidence Intervals o A 90% confidence interval for a parameter Z is an interval that is constructed using a method that gives intervals containing the true value of Z, 90% of the time o Suppose (12.2, 17.8) is a 55% conf
MATH 226 October 31, 2007 First notes: 2:27pm Know for test o How to plot distributions using Minitab o How to vary the parameters using Minitab o How to run simulations to find experimental distributions using Minitab o How to read and alter histo
MATH 226 October 29, 2007 Functions of random variables o Two variables are independent if the measurement for one does not depend on the measurement for the other one for the same object o Theorem Let Xij,., Xn be random variables and a0, a1, .,
MATH 226 October 24, 2007 Exponential Distribution o X = waiting time to the first event (of a Poisson Process) o f(x) = (1/)e-x/, x > 0, > 0 F(x) = P(X x) = 0x(1/)e-t/dt = 1 e-x/, x 0 o EX = , VarX = 2 Erlang Distribution o X = waiting time t
MATH 226 October 22, 2007 Normal Distribution o Gaussian Distribution (bell-shaped) o
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o inflection at one standard deviation o = EX = sqrt(Var(x) f(x) = (1/sqrt(2) )e^-(x )2/22 o the larger the standard deviation is the more narrow the d
MATH 226 October 17, 2007 Continuous Random Variables
Probability density Function (PDF) o A function of all reals with the properties f(x) 0 - f(x)dx = 1 o for a continuous random variable x with pdf f(x) we say: P(a x b) = the integral fro
MATH 226 October 10, 2007 Random Variable in example 18 of worksheet o X = number of sprinklers out of the full 10 that do work X ~ binomial(10, 0.9) o P(x 8) = P(x=8) + P(x=9) + P(x=10) = 10x=8(10 choose x)(0.9)x(0.1)10-x = 0.929809 On the calc
Robert Boyle described elements as a substance that could not be broken down any further Law of Mass Conservation Matter cannot be created nor destroyed Law of Definite Proportions Pure substances of the same thing always contain the same proporti