Verified Certificate

Supported by the following organizations

This is to certify that Bryan Thomas Karazsia successfully completed and received a passing grade in PH125.3x: Data Science: Probability a course of study offered by HarvardX, an online learning initiative of Harvard University.

Noted by

Rafael Irizarry

Rafael Irizarry

Professor of Biostatistics Harvard T.H. Chan School of Public Health

About edX

edX offers interactive online classes and MOOCs from the world’s best universities, including MIT, Harvard, Berkeley, University of Texas, and many others. edX is a mission driven initiative created by founding partners Harvard and MIT.

About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.