College Probability & Statistics Tutoring

Common topics in Introductory Statistics:

Visualizing and describing data, the normal (gaussian) distribution, introductory probability, probability distributions, statistical inference, hypothesis testing, confidence intervals, correlation, linear regression, p-values, chi-square tests. 

Introductory statistics classes are often required by many majors, and usually are intended to expose you to a broad range of statistical topics while also doing some programming in Excel, R, or Python. It’s usually a lot of general information thrown at students that changes topics every week, and requires drawing from various areas of math. It can be overwhelming, but it doesn’t have to be. 

Here are some tips from our expert statistics tutors: 

Probability: Singular values from a discrete probability distribution (like Poisson or Binomial) can have a non-zero probability, P(X=x) > 0, because the possible values a discrete random variable can take are finite. However, a continuous probability distribution (like the Normal) can always have infinite possible values, so the probability of any single value is always 0!

Confidence intervals and p-values: Students often fail to see a critical connection between p-values and confidence intervals from the same hypothesis test. If a confidence interval contains the null hypothesized value, then the p-value will be larger than the significance level (and vice versa). Similarly, if a confidence interval does not contain the null hypothesized value, the p-value will always be smaller than the significance level. 

Data Analysis/Programming Tutoring

Common topics in Data Analysis/Programming:

R, Python, Excel, barplots, histograms, data visualization, simple linear regression, two-sample comparisons, ANOVA, multiple linear regression, dummy variables, variable selection, AIC, BIC, logistic regression, categorical data analysis

Data analysis via programming is the practical component of statistics. When you have real data that needs to be analyzed, programming gives you the ability to efficiently generate visualizations and analysis reports. Our tutors can help you bridge the gap between coding and the mathematical concepts of statistics you’ve learned in an introductory course.

Here are some tips from our expert statistics tutors:

General programming: Treat learning statistical programming like you would learning a language: focus less on the specific functions you are using, and more on the syntax and formatting that forms it. If you can understand how to approach it as a language, you’ll have a much easier time coding.

Be a great “question asker”: Almost everything you need to know to program in R, Python, or Excel can be googled. The more difficult aspect is being able to know how and what to search in Google. Our tutors can help you understand how to formulate what your objectives are when coding and how these might best be searched when searching the internet for code ideas. 

Probability Theory Tutoring

Common topics in Probability Theory:

Probability spaces and models, random variables, law of total probability, Bayes theorem, densities, distributions, independence, laws of expectation and variance, law of large numbers, central limit theorem, moment generating functions, stochastic processes.

If you’re taking this course, you’re probably a statistics or math major. What makes probability theory difficult is it moves away from a tangible realm of statistics to a more abstract area of math. We can help you recall the critical axioms, theorems, and properties you’ve learned from past math classes (such as calculus and analysis) to keep your probability theory a little more grounded. 

Here’s a tip from our expert statistics tutors:

To solve any probability problem, follow the PROB rule: 

Problem: Make sure you fully understand the problem statement, what is it asking for and what is the final objective? 

wRite: Write down everything that is known from the problem statement, such as whether two random variables are independent, what the variance of a random variable is, etc…

Organize: Organize a list of theorems, properties and other knowledge that might be relevant to the problem, and note which information from the problem statement it might be relevant to. 

Begin: Begin working and don’t be afraid to make mistakes, now that you have all the available information organized. Make sure each step doesn’t violate any laws of probability.

Mathematical Statistics Tutoring

Common topics in Mathematical Statistics:

Probability, random variables, laws of expectation and variance, discrete and continuous probability distributions, sampling distribution, central limit theorem, multivariate distributions, estimation, estimator properties, advanced hypothesis testing and confidence intervals, etc…

Mathematical statistics is often one of the hardest courses a statistics major will take as an undergrad. Hopefully you’ll have math experience from classes like calculus and linear algebra, but it can still be difficult not to get lost in all the notation, greek letters, and new theorems. 

Here are some tips from our expert statistics tutors: 

Probability distributions: make sure you understand the “chemistry” of a probability distribution, such as how it is made up of parameters, it can be continuous/discrete, it is defined by a cumulative density function, etc…Rather than memorizing every single probability distribution (Poisson, Binomial, Exponential, …), focus on what makes up the structure of these distributions!

General math: Mathematical statistics relies on a variety of math, from algebra to differential and integral calculus to linear algebra. Make sure that you don’t get lost in the tedium of having to solve problems using so many different types of math. You are in the class to learn about the laws and theorems of advanced statistics. However, at the same time, proceed with any algebra or calculus rules with caution and take your time.