PDF4PRO ⚡AMP

Modern search engine that looking for books and documents around the web

Example: biology

Lecture 4: Random Variables and Distributions

Lecture 4: RandomVariables and DistributionsGoals Working with Distributions in R Overview of discrete and continuousdistributions important in genetics/genomics Random VariablesRandom Variables ! "01-1A rv is any rule ( , function) that associatesa number with each outcome in the samplespaceTwo Types of Random Variables A discrete Random variable has acountable number of possible values A continuous Random variable takes allvalues in an interval of numbersProbability Distributions of RVsDiscreteLet X be a discrete rv. Then the probability mass function (pmf), f(x),of X is:! f(x)=P(X = x), x 0,x Continuous! P(a"X"b)=f(x)dxab#Let X be a continuous rv. Then the probability density function (pdf) ofX is a function f(x) such that for any two numbers a and b with a b:abAaUsing CDFs to Compute ProbabilitiesContinuous rv:! F(x)=P(X"x)=f(y)dy#$x%pdfcdf! P(a"X"b)=F(b)#F(a)Using CDFs to Compute ProbabilitiesContinuous rv:! F(x)=P(X"x)=f(y)dy#$x%pdfcdf!

•This implies that until data is collected, any function (statistic) of the observations (mean, sd, etc.) is also a random variable •Thus, any statistic, because it is a random variable, has a probability distribution - referred to as a sampling distribution •Let’s focus on the sampling distribution of the mean,! X

Fullscreen Download
Loading..

Tags:

  Distribution, Functions

Information

Domain:

Source:

Link to this page:

Please notify us if you found a problem with this document:

Spam in document Broken preview Other abuse

Transcription of Lecture 4: Random Variables and Distributions

Documents from same domain

Lecture 10: Multiple Testing - UW Genome Sciences

www.gs.washington.edu

Why Multiple Testing Matters Genomics = Lots of Data = Lots of Hypothesis Tests A typical microarray experiment might result in performing 10000 separate hypothesis tests.

  Tests, Multiple, Testing, Hypothesis, Hypothesis tests, Multiple testing

DNA Isolation from Strawberries

www.gs.washington.edu

source for extracting DNA because they are easy to pulverize and contain enzymes called pectinases and cellulases that help to break down cell walls. And most important, strawberries have eight copies of each chromosome (they are octoploid), so there is a lot of DNA to isolate. The purpose of each ingredient in the procedure is as follows:

  Form, Isolation, Strawberries, Extracting, Dna isolation from strawberries

Lecture 10: Multiple Testing

www.gs.washington.edu

False Discovery Rate m 0 m-m 0 m V S R Called Significant U T m - R Not Called Significant True True Total Null Alternative V = # Type I errors [false positives] •False discovery rate (FDR) is designed to control the proportion of false positives among the set of rejected hypotheses (R)

  Rates, Discovery, False, False discovery rates

Lecture 7: Hypothesis Testing and ANOVA

www.gs.washington.edu

•Calculate a test statistic in the sample data that is ... candidate gene. We then divide these N individuals into ... Sum of MS F Squares Source of df Variation! SST G k"1! SST E N"k! SST G k"1 SST E N"k. Non-Parametric Alternative • Kruskal-Wallis …

  Samples, Candidate

I-9 Form: Instructions for Nonresident on H-1B or TN Visa

www.gs.washington.edu

I-9 Form: Instructions for Nonresident on H-1B or TN visa Instructions for both New Hires and Updating & Reverification For more detailed information about completing Form I-9, employers and employees should refer to the Handbook for Employers: Instructions for Completing Form I-9 (M-274). _____

  Form, Visa

Lecture 5: Estimation - University of Washington

www.gs.washington.edu

Bayesian Estimation: ÒSimpleÓ Example ¥I want to estimate the recombination fraction between locus A and B from 5 heterozygous (AaBb) parents. I examine 30 gametes for each and observe 4, 3, 5, 6, and 7 recombinant gametes in the Þve parents. What is the mle of the recombination fraction? ¥Tedious to show Bayesian analysis. LetÕs simplify ...

  Estimation

Lecture 9: Linear Regression - University of Washington

www.gs.washington.edu

Lecture 9: Linear Regression. Goals • Linear regression in R •Estimating parameters and hypothesis testing ... •Previous coding would result in colinearity •Solution is to set up a series of dummy variable. In general for k levels you need k-1 dummy variables x 1 …

  Lecture, Previous

1. Plasmid structure 2. Plasmid replication and copy ...

www.gs.washington.edu

Plasmid replication requires host DNA replication machinery. 2. Most wild plasmids carry genes needed for transfer and copy number ... Large or small region of homologous DNA cloned that will integrate into the chromosomal target. 5. Need a counter selection method to kill the donor cells 6. Screen for what you think is correct.

  Regions, Replication

Lecture 2: Descriptive Statistics and Exploratory Data ...

www.gs.washington.edu

Multivariate Data •Organize units into clusters •Descriptive, not inferential •Many approaches •“Clusters” always produced Clustering Data Reduction Approaches (PCA) •Reduce n-dimensional dataset into much smaller number •Finds a new (smaller) set of variables that retains most of the information in the total sample

  Data, Multivariate, Multivariate data

Related documents

Lecture: Probability Distributions

www.ssc.wisc.edu

The distribution function has the same interpretation for discrete and continuous random variables. The CDF is also sometimes called the distribution function (DF). x Requirements for CDFs (1) Fx()≥0 everywhere the distribution is defined (2) Fx() non-decreasing everywhere the distribution is defined. (3) Fx()→1 as x →∞ 1

  Distribution, Functions, Distribution function

The Truncated Normal Distribution

people.sc.fsu.edu

Note that the standard deviation of any distribution, represented by std(ˆ()), is simply the square root of the variance, so for the standard normal distribution, we also have that std(˚(0;1;)) = 1. 1.3 The Cumulative Distribution Function Recall that any probability density function ˆ(x) can be used to evaluate the probability that a random

  Distribution, Functions, Normal, Distribution function, Truncated normal distribution, Truncated

The Multivariate Gaussian Distribution

cs229.stanford.edu

Recall that the density function of a univariate normal (or Gaussian) distribution is given by p(x;µ,σ2) = 1 √ 2πσ exp − 1 2σ2 (x−µ)2 . Here, the argument of the exponential function, − 1 2σ2(x−µ) 2, is a quadratic function of the variable x. Furthermore, the parabola points downwards, as the coefficient of the quadratic term ...

  Distribution, Functions

DISCRIMINANT FUNCTION ANALYSIS (DA)

userwww.sfsu.edu

Normal distribution: It is assumed that the data (for the variables) represent a sample from a multivariate normal distribution. You can examine whether or not ... discriminant function coefficients will not reliably assess the relative importance of the predictor variables.

  Distribution, Functions, Discriminant, Discriminant function

Lecture 15: Order Statistics - Duke University

www2.stat.duke.edu

Beta Distribution The Beta distribution is a continuous distribution de ned on the range (0;1) where the density is given by f(x) = 1 B(r;s) xr 1(1 x)s 1 where B(r;s) is called the Beta function and it is a normalizing constant which ensures the density integrates to 1. 1 = Z 1 0 f(x)dx 1 = Z 1 0 1 B(r;s) xr 1(1 x)s 1dx 1 = 1 B(r;s) Z 1 0 xr 1 ...

  Distribution, Functions

Inverse Gamma Distribution

www.johndcook.com

the inverse gamma distribution prevents having to repeatedly apply the transformation theorem in applications. Here we derive the distribution of the inverse gamma, calculate its moments, and show that it is a conjugate prior for an exponential likelihood function. 1 Parameterizations There are at least a couple common parameterizations of the ...

  Distribution, Functions

Related search queries

Distribution Function, Distribution, Truncated Normal Distribution, Function, Discriminant function