Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.
A standard statistical procedure involves the collection of data leading to test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
Homework Statement
Suppose you take a pass-fail test repeatedly. Let Sk be the event that you are successful in your kth try, and Fk be the event that you fail the test in your kth try. On your first try, you have a 50% chance of passing the test.
P(S1)=1−P(F1)=1/2.
Assume that as you take the...
Homework Statement
50 students live in a dormitory. The parking lot has the capacity for 30 cars. If each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars?
Homework Equations
P(A) =...
Homework Statement
For reference, this is the image setting up the problem.
"A wireless sensor grid consists of 21×11=231 sensor nodes that are located at points (i,j) in the plane such that i∈{0,1,⋯,20} and j∈{0,1,2,⋯,10} as shown in Figure 2.1. The sensor node located at point (0,0) needs...
There is so much variation amongst statistics majors across schools. I think it is the major that varies the most. This is surprising, since statistics is math. A big reason for this is that sometimes it is offered from math department, and others from the business department (stern's stats...
If business degrees require only intro to stats class that contains no calculus, and stats could be summarized into a short, easy, one semester course, are taking calculus-based statistics courses after intro to stats helpful for decision making, or are the calc-based stats courses merely just...
Homework Statement
In a 52 card deck, if you draw 5 cards find the probability of drawing exactly one ace.
Homework Equations
(n k) = n!/k!(n-k)!
P(A) = |A|/|S|
The Attempt at a Solution
So I took the logic of a different example we had that stated it like this - If we have 5 options but...
Homework Statement
Let A and B be two events such that
P(A) = 0.4, P(B) = 0.7, P(A∪B) = 0.9
Find P((A^c) - B)
2. Homework Equations
I can't think of any relevant equations except maybe the Inclusion Exclusion property.
P(A∪B) = P(A) + P(B) - P(A∩B)
This leads us to another thing
P(A∩B^c)...
http://oi58.tinypic.com/2d85aix.jpg
above is an url to the stats major program at my school. In red are the two classes that overlap. Is it likely that the overlap is intended, or a typo? Do universities ever allow such overlap (an emphasis class overlaps with a core class)?
They changed it a...
is comp sci minor worth it for stats major? Does it significantly boost value on the labor market?
Is it worth an extra year of school? Also, I'm 22 and feel left behind from my peers, who have graduated.
Could you please list and elaborate as much as you can on schools that are heavy on the theoretical side of statistics? Thank you as I have to have my applications in by December-January for grad school (I plan to enter a PhD program and would like guaranteed funding).
Question
Find the posterior probability that the next two observations y4 and y5 will both be zero? Where the prior distribution is a gamma with parameters (a,b) and the sample is of size of 3 taking from a poisson disribution with parameter V.
So far I have shown that the posterior...
Hey guys, nice to meet you all! My name is Jonathan and I'm from Queensland Australia.
I'm currently working on a project which is seeking to find the most accurate method to value an asset based on historical stats. I think the best way to describe would be to provide a theoretical example:
I...
< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >
Hi everyone,
Got a stats question here from my revision material, but I am not sure if I've answered the whole question or not...
Hi, I will be majoring in Statistics at SFSU. However, while the curriculum is that of an Applied Statistics major (below is a link to a chart of the three offered emphasis, which we must choose one of out of ). Why, then, does the school call it "Statistics" instead of "applied Statistics"? And...
till now i used the normal method for finding out the mode of a given data that is just simply look for the most frequently occurring observation and label it as the mode. But recently I have encountered another method for finding out the mode in which it was also stated that my old method for...
I am beginning a second undergraduate degree this fall and am trying to decide on a major but don't think I have enough information to discriminate between my top two choices.
My first degree was in mathematics education (where I developed a deep appreciation for math). I have interests in...
Homework Statement
Here is a small part of an EESEE data set, "Nutrition and Breakfast Cereals," that describes the nutritional content per serving of 77 brands of breakfast cereals:
What are the individuals in this data set?
For each individual, what variables are given? Which of these...
This is probably a stupid question , but,
It's easy enough to show that the mle of a poission distribution is ## \bar{x}##: ## \hat{ \lambda}= \bar{x} ##
But,I'm then looking at the generalized ratio test section of my book, multinomial, it esitmates ## \lambda ## for some data by ## \sum...
Thank you in advance. I need to know how to do these 3 problems by tomorrow in order to pass my AP stats class. Please help!
1.Your friend is playing Monopoly and is in desperate straits. He is cashless and has just landed in jail. He must either roll a double to get out free or pay $50...
Hey I am new here and not exactly sure how it works. I am stuck on this problem from my professor and would love any help anyone has!When one thinks of the normal distribution the first thing that comes to mind is the bell curve and grades. While this is one example of a normal curve that is...
Homework Statement
Let n and k be positive integers such that both n and n − k are large. Use Stirling’s formula to write as simple
an approximation as you can for Pn,k.
Homework Equations
## \lim_{n \rightarrow \infty} {(2 \pi)^{1/2}n^{n+1/2}e^{-n} \over n!} = 1 ##
The Attempt at a Solution...
Leisure Time In a Gallup poll: 1010 adults were randomly selected and asked if they were satisfied or dissatisfied with the amount of leisure time
that they had. Of this sample 657 said that they were satisfied and 353 said that they were dissatisfied. Use a 0.01 significance level to test the...
Hi everyone.
It's been years since I've done any stats, so I need a bit of help, please. I want to include it in a blog post I'm going to do (not here on PF), so I don't want to give away too many details :p I apologise for my terrible understanding of stats, please be patient!
Anyway, over...
Hey everyone,
This may be of interest for those of you looking to pursue Medical Physics in grad school.
I spent a little while making a shiny app displaying CAMPEP statistics, including enrollment data and employment post graduation.
https://joelcarlson.shinyapps.io/campep/
Something that...
Homework Statement
What is reduced density matrix ##\rho_A## and the Bloch vector representation for a state that is 50% ##|0 \rangle## and 50% ##\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)##Homework Equations
The Attempt at a Solution
[/B]
I haven't seen many (any?) examples of this so I'm...
I am trying to use Bayesian methods (Bayes rule) to predict further datapoints (at point n,n+1,n+2 etc..)...
I begin by generating a normal pdf using previous 75 datapoints (prior: n-75 to n-1) with mean value, μ: 1.25 and standard deviation, δ: 3.67.
Note: previous datapoints range from...
Hello, PF!
[My question pertains to a non-rigorous, undergraduate introductory Probability and Statistics course. I'm no math major, so please correct me if I've mishandled any terms or concepts as I try to express myself. I'm always eager to learn!]
* * *
In a discussion of the...
Hello Everyone,
As a long-time University Teaching Assistant in Statistics, I have recently launched a YouTube Channel with the idea of providing help for students who are taking courses in introductory statistics and probability. The videos it contains are the online equivalents of the Review...
Hello,
I'm not sure if this is the correct section to post this in, but I need some help with my graphing calculator. I also posted this in the Statistics section.
I am given a set of X and Y data (2 sets of numeric data) and I need to find out how to find the Sxx, Syy, and Sxy in my TI84...
I worked out the Planck Black-Body Radiation Formula using Bose-Einstein Statistics, but I feel there is something conceptual I am missing here.
When Planck derived the formula, he started out with the Boltzmann distribution function, and assumed that there were discrete energy levels...
Homework Statement
I have no idea where the sum of x^2 comes from, from the information I posted. I know it must be something pretty simple but its completely going over my head. In the picture that I've attached, I am wondering where the 2431.72, 4901.66, and 3252.44 come from. Thank you...
Homework Statement
An investor wants to purchase one investment among common stocks, preferred stocks and bonds of six industries located in several countries. The investor can use a full-service broker or a discount broker and can buy with cash or margin. If there are 288 possible choices...
This is a two-fold statistical thing I want to pursue and I'm unsure of which test(s) to use. Using data of gender and age at time of death from a large, old cemetery in town I want to compare two things:
1. Average life expectancy of citizens of our town compared to the national average
2...
Homework Statement
A word has n letters, in which one of those letters is present a times and another is present b times (all other letters are present only once).
a.) How many combinations of x letters are there from this word?
b.) How many arrangements of x letters are there from this word...
1. I know var(x)=E(x^2)-E(x)^2; is there a repeated way to use this to attain var(x^2)? Or how in general, without resorting to integration, can I calculate it?
2. We typically deal with "i.i.d random variables X_i" and do things like find var(X) given E(X^2) etc..it never occurred to me...
Sorry I need help in a hurry. This is for work and I haven't done this in a long time.
I have a population of ~ 5,338,000
And I know 0.74% respond to something.
I want to know if a population of only 5,000 will respond better or worse than my 5 million.
I am worried that it is too...
Homework Statement
You have 5 identical boxes that stand one after another. How many different ways can you put your 3 identical eggs into these boxes?
For whatever reason, my physics professor decided to give us this as a problem to think about in how to solve. However, from my...
Edit: I had no idea what I was doing when I posted this here, sorry! Could someone move it to the Maths help forum?
I have a few basic stats questions which I'd appreciate if someone could help me answer. These are conceptual really.
a) Often I'm asked to come up with a graph which has a...
Homework Statement
Let x be the number of successes in n independent Bernoulli trials, each one having unknown probability θ of success. Assume θ has prior distribution θ ~ Unif(0,1). An extra trial, z, is performed, independent of the first n given θ, but with probability θ/2 of success. Show...
Homework Statement
Question 3 here: http://www.stat.washington.edu/peter/395/samplemidterm.pdf
Solution to it here: http://www.stat.washington.edu/peter/395/prmt.sln/sln.html
By the way, I could use help soon since this is the practice exam for an exam I'm taking 7 hours from now...
Please help me with multiple comparisons - urgent (stats)
Hello, I just have a quick question understanding multiple comparisons and I'd appreciate any help because I'm on the verge of failing :rolleyes: I'm reviewing for a test, and reading over questions and their corresponding answers in the...
Hi all,
This post will be long, but I hope in giving more relevant information, the replies will be more helpful. Apologies for the length, and thanks for reading, given now. I'll state the question here though to avoid you having to search for it:
Does it make any real difference whether...
Homework Statement
Let X ~ Exponential(3) and Y ~ Poisson(5). Assume X and Y are independent. Let Z = X + Y. Compute the Cov(X,Z).Homework Equations
I know Cov(X, Z) = E(XZ) - E(X)E(Z). But how do I compute E(XZ) and E(Z) ?? Since for E(XZ), I would need the pdf/pmf (Exp is abs cts, while...
1. Homework Statement [/b]
A barber shop has two chairs to cut hair and 10 people per hour enter the barbershop to get a haircut. . The average time it takes to get a haircut is 6 minutes. On this particular day, only one barber is cutting hair. Customers that enter the barber shop and use the...
Homework Statement
So the question is, given a set of random numbers, find the mean and the value that will be >= 99% of the occurances. So for a set of random numbers between say, 1-100, if the mean is 50, how do I find out what number will be >= 99% of all observations of the time...
Homework Statement
Suppose that I'm collecting cards, and that in a complete collection there are m items.
When buying a new card, there's an equal probability that the card is any of those m cards.
Let X be the number of cards I need to buy in order to get a complete collection...
Consider a uniform distribution on the interval 0≤ X ≤ θ. We are interested in estimated θ from a random sample of draws for the PDF. Two potential estimators are:
θ1 = (2/n) Ʃ Yi
and
θ2 = (n/θ)(y/θ)^(n-1)
which estimator would you prefer and why? What statistical properties did you...
I'll offer a digest version of my earlier post that appeals to shorter attention spans.
I'm considering the pursuit of a graduate degree in statistics. My CV in a nutshell:
Math Major: 3.6 GPA (in major)
GRE: 159 V / 167 Q
Research experience: Summer Institute in Biostatistics (SIBS)...