# IOE 265 Study Guide - Final Guide: Standard Deviation, Covariance, Central Limit Theorem

by OC2294430

Department

Industrial And Operations EngineeringCourse Code

IOE 265Professor

Xiuli ChaoStudy Guide

FinalThis

**preview**shows half of the first page. to view the full**2 pages of the document.**Confidence Intervals: Identify a plausible

range for point estimate

Ex. 95% confidence range implies 95% chance

that true value is in range

Find multiplier with invNorm(,0,1)

Use sample std. dev of

Note: Sum of independent normal random

variables leads to and

For probability we have:

For one-sided CI (u):

For all mean CI:

Note: round-up, width is ½ of interval

Must know variance + normal dist.

Central Limit Theorem: When n is large

enough (, distribution of sample mean is

approx. normal ( )

Proportion Estimation: Bernoulli:

CI:

Note: For n, use p and q as .5 to be safe

Chi-Squared Distribution: If population has

normal distribution then:

has normal dist. Mean Variance

Sample Variance

is Chi-

Square Distributed with n-1 df

If Z is standard normal, and

is Chi-Square

dist. with n degrees freedom:

is t-dist with n df

T-Distribution: Area under curve to the right

of t critical value is

Norm w/out mean and variance, small sample

CI:

CI for variance

Hypothesis Testing: Make a claim

Reject or fail to reject that claim

Null hypothesis:

Alternate hypothesis:

1: Fix level of significance, acceptable prob of

rejecting null when it’s true

2: Compute prob. of observing sample, take z-

value and turn into p-value

3: If p-value is smaller than sig. level, reject

null hypo, otherwise fail to reject

You need:

Null and alternative hypothesis

Test statistic – what decision is on

Rejection region (when to reject)

Significance level : probability, given

hypothesis is correct, of rejecting it

Type II error is Beta, fail to reject + H0 false

Reject the null if p-value < alpha (smaller p-

value is stronger evidence against H0)

Mu0 is actual and mu’ is test

Note: smallest level of signiﬁcance at which

you would be willing to reject the null

hypothesis is the P-value.

Definitions: Probability – measure of

likelihood for something to occur. Statistics –

concerned with learning from data. Types:

categorial (qualitative) numerical (quantitative)

Univariate: observations on 1 variable

Bivariate: observations on 2 variables

Discrete: Finite possible values

Continuous: any real value in interval

Dot plot: each datapoint is dot on a line

Stem&Leaf: First part of each piece of data on

left hand (stem) side. Remaining digits on

right-hand (leaf) side in order. Add a key

Frequency Analysis: # of frequencies of each

class/value in data set (relative, cumulative)

# of ranges is , 5-20

Histogram is graphical rep. for 1 variable

(exponential, normal, bi-modal, skewed)

Graph of rel. freq w/ width 1 is samp density

Density:

Median: middle obs., further from skew

Trimmed mean: Eliminate % of values from

both ends, re-compute mean

Fourth spread (IQR): Upper 4th – Lower 4th

Outlier is 1.5*IQR from closest 4th, Extreme

Outlier is 3*IQR away (open circle)

Mode: most common, Range: max-min

sample uses N-1

Part 2 Mod 1: Sample space: set of all

possible outcomes. Events: any subset of

sample space. Probability: likelihood of event

A\B is

N1 possible outcomes then N2 = N1*N2

Permutation (w/order):

Combination (w/out order):

P(A|B)

Independence:

Discrete RV (pmf):

Cumulative:

Expected value:

E(ax+b)=aE(x) +b, V(ax+b) = a2V(x)

V(x =

Bernoulli: E(x) = p, V(x)=p(1-p)

Binomial: Bin(n,p): n=number of trials,

p=prob of success is

Multiple Bernoulli becomes binomial

E(x) = np, V(x)=np(1-p)

Geometric: Number of independent B trials

until success p(x)=(1-p)x-1p, E(x) = 1/p,

V(x) = (1-p)/p2, P(

Hypergeometric: Batch has N products, M

good and N-M bad, pick N products, prob of x

good: h(x:n,M,N) =

E(x) = np, V(x)=

, p=

find more resources at oneclass.com

find more resources at oneclass.com

###### You're Reading a Preview

Unlock to view full version