×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

by: Jordyn

27

0

2

# Exam 2 formula sheet STT 315

Marketplace > Michigan State University > Business > STT 315 > Exam 2 formula sheet
Jordyn
MSU
GPA 3.6

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

formula sheet
COURSE
PROF.
Eroglu
TYPE
Study Guide
PAGES
2
WORDS
CONCEPTS
Math, Statistics, Stats, formula, stat formulas
KARMA
50 ?

## Popular in Intro to Business Statistics

This 2 page Study Guide was uploaded by Jordyn on Friday April 1, 2016. The Study Guide belongs to STT 315 at Michigan State University taught by Eroglu in Fall 2015. Since its upload, it has received 27 views. For similar materials see Intro to Business Statistics in Business at Michigan State University.

×

## Reviews for Exam 2 formula sheet

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 04/01/16
Random variable (rv) is a numerical variable whose value depends on chance—values are associated with outcomes of a random experiment where one and only one numerical value is assigned to each sample point  Discrete—if it either takes finitely many or countable infinitely many values (its numbers can be enlisted in an infinite sequence)  Continuous—if The set of possible values X can take is either an interval or a disjoint union of intervals on real line—if it can assume unaccountably many values o Example: total amount of rainfall Discrete random variable: P (x ≤ 1) Probability distribution function: P(x)= P(X=x) Expectation: μ = E(x) =Σ xp(x) P (x > 12) = 1 – P (x ≤ 12) Variance: σ = E[(x-μ) ] = Σ(x-μ) p(x) P (x < 3) = p (x ≤ 2) 2 P (x < 7) = P (x ≤ 7) – p (x = Standard deviation σ = +√σ For any real numbers a and b 7)  E(aX ± b) = aE(X)±b P (x≥3) = 1 – P (x ≤2) P (2 ≤ x ≤ 4) = P(x ≤ 4) –  σ(aX±b) = |a|σ(X) BINOMIAL Characteristics for binomial experiment: The experiment consists of n identical trials, There are only two possible outcomes on each trial – ‘success’ and ‘failure’, The probability of success remains the same from trial to trial, The trials are independent (n), The binomial random variable X is the number of successes in n trials, X assumes values 0,1,2… ,n. (Non-negative whole number) P(x)=( xp q n-x p(x)=P(X-x)= probability of x successes, n= number of trials, x= number of successes in n trials, (x=0,1,…,n), n-x=number of failures, p=P(sucess), and q=P(failure)=1-p binomcdf(n,p,x)  mean: μ=np 2  variance: σ =npq  standard deviation: σ = √npq POISSON Characteristics of Poisson random variable: The experiment consists of counting number of times an event occurs during a given unit of time or in a given area or volume (any unit of measurement), The probability that an event occurs in a given unit of time, area, or volume is the same for all units, The number of events that occur in one unit of time, area, or volume is independent of the number that occur in any other mutually exclusive unit, The mean number of events in each unit is denoted by λ, a positive real number -λ x P(x)=e *(λ /x!) p(x) = P(X=x) given λ, λ = mean (expected) number of events in unit, e = 2.71828 … (base of natural logarithm), x = number of events per unit Poissonpdf (λ,x) = poissonpdf (mean, x-value)  μ = E(X) = λ  σ = √λ the mean number of events in each unit is λ > 0 HYPERGEOMETRIC RANDOM VARIABLE The hypergeometric random variable X is the number of successes in the draw of n elements p(x) probability of x successes, N = total number of elements, r = number of successes in the N elements, n = number of elements drawn, x = number of successes in the n selections, where max {0, n – (N -r)} ≤ x ≤ min {r, n}  μ = nr/N  σ = r(N-r)n(N-n) 2 N (N-1) In calculator (r)= n nCr r Sampling with replacement vs sampling without replacement r elements are successes, and N − r are failures In with replacement sampling the selected objects are returned to the population before each draw—binomial distribution with n and p = r/N In without replacement sampling the selected objects are NOT returned to the population before each draw— hypergeometric distribution with parameters N, r, and n NORMAL DISTRIBUTION Can be used to approximate discrete probability distributions—empirical rule is based on normal distribution In many data-sets, the histograms are roughly symmetric, unimodal and bell-shaped, these distributions are usually modeled by normal distribution Location of normal distribution is determined by μ Dispersion of normal distribution is determined by σ Normalcdf (a, b, μ, σ)—a: lower bound, b: upper bound, μ: mean, σ: standard deviation To find the area : p invNorm (p, μ, σ)—area: enter the value of p, μ: mean, σ: standard deviation We want to find x 0invNorm is used when areas is given but want to find a number on the horizontal line Used to find area to left (x ≤ 6) ex: below what height—means the area to the left Standard normal distribution: μ=0 and σ=1, if μ and σ aren’t specified μ=0 and σ=1 so a= z and b1= z 2 Z score = x-μ p(x≤a): z = (a+0.5) – μ σ σ if given z score and asked to find the area to the left normalcdf(-9^99, z-score) Normal approximation of binomial distribution Use z-scores If n is very large (theoreticallyn∞), then the probability distribution of X is approximately normal with mean µ = np and standard deviation σ = √npq where q=1-p Continuity correction is required-- P(X≤x) ≈ P(Normal ≤x – 0.5), P(X=x) ≈ P(x-0.5 ≤ Normal ≤ x + 0.5) If the interval np±3√npq is contained in the interval (0,n) then n is “large enough” Are the data normally distributed Examine a normal probability plot for the data. If the data are approximately normal, the points will fall (approximately) on a straight line Uniform probability distribution Continuous random variables that appear to have equaly likely outcomes over their range of possible values posses a uniform probability distribution—looks like a box If x is a uniform rv in the interval (c,d) then p(a<x<b) = (b-a)/(d-c) If c ≤ a < b ≤ d:  μ = (c+d)/2  σ = (d-c)/ √12 Exponential probability distribution function If x is an exponential rv with mean σ, then p(x>a) = e -a, a>0 –a/θ -b/θθ P(a<x<b) = e - e , 0 < a< b μ = θ, σ = θ

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Jim McGreen Ohio University

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Amaris Trozzo George Washington University

#### "I made \$350 in just two days after posting my first study guide."

Jim McGreen Ohio University

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com