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Advice for fulfilling CMU's pre-req and strengthening math&stat background

Hi everyone,

Thank you very much for your time and help here. I'm writing here to seek you advice for fulfilling CMU's pre-req and strengthening math&stat background

My math and statistics classes taken in college include Calculus, Linear Algebra, and Differential Equations so I'm looking to take the calculus-based probability course through online extension schools. There are two options I found so far and both of them cover the topics listed in CMU's FAQ section. I listed them at the bottom. Which of them do you all think will be a better fit for CMU's requirement.

"If you have not previously taken a calculus-based probability course, you should look for a course covering advanced topics in probability including the law of large numbers, the central limit theorem, moment-generating functions, multivariate probability distributions, conditional distributions, and independence, covariance and correlation of random variable." - From CMU MSCF website

As a non-math major and a reapplicant, I recognized that I had weakness in my math and stat background. I will be very grateful for any information and advices on accredited math classes that I could take to strengthen my profile. I'm also planning to retake linear algebra because I only got a B+ for it in college. I'm looking at the class linear algebra for machine learning on UC San Diego Extension. If there is any coursework you would recommend, I couldn't appreciate it more if you let me know. Thank you very much again for your help here!

MATH E-156 Mathematical Statistics (Harvard Extension School)
MATH E-156 Mathematical Statistics | CRN 16470 - Harvard Extension Course Catalog

This course is an introduction to mathematical statistics and data analysis. It starts by introducing central concepts of probability theory (events, probability measure, random variables, distributions, joint distributions, and conditional distributions) and then moves on to the development of mathematical foundations of statistical inference. Topics covered in the course include random variables, expectations, parameter estimation (method of moments, method of maximum likelihood, and Bayesian approach), properties of point estimators (bias, variance, consistency, and efficiency), confidence intervals, hypotheses testing, likelihood ratio test, data summary methods, and introduction to linear regression. A class of distributions, including chi-squared, t, and F distributions, the distributions derived from normal that occur in many applications of hypothesis testing and statistical inference, are introduced.

MS&E220 Probabilistic Analysis (Stanford Online)
Probabilistic Analysis | Stanford Online

Probability theory is essential to many human activities that involve the quantitative analysis of large sets of data. This fast-paced course provides an understanding of uncertain phenomena using probability theory. Develop conceptual and intuitive insights into probabilistic reasoning and the ability to understand and solve real world problems. Learn the concepts and tools for the analysis of problems under uncertainty, focusing on model building and communication including the structuring, processing, and presentation of probabilistic information. Use spreadsheets to illustrate and solve problems to complement analytical closed-form solutions.
 
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