Verified Certificate

Supported by the following organizations

This is to certify that Karan Ketankumar Thakkar successfully completed and received a passing grade in 416.1x: Probability: Basic Concepts & Discrete Random Variables a course of study offered by PurdueX, an online learning initiative of Purdue University.

Noted by

Mark Daniel Ward

Mark Daniel Ward

Associate Professor, Purdue University Associate Director, Center for Science of Information Purdue University & Center for Science of Information

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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.