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What is the difference between

A Random Variable is a variable which represents the outcome of a random experiment.

and

A Random Variable is a variable that represents the outcome of a random experiment.

?

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    In those two sentences, there is no difference. The restrictive relative clause that/which represents the outcome of a random experiment has its relative pronoun as subject (so it must be present, and can't be deleted as usual, because subject NPs are required in English), and that relative pronoun may be either that or which, since the relative clause is restrictive. If the relative clause were non-restrictive, like the one in a random variable, which is a term referring to a non-constant memory location, then which would be required, and that would be ungrammatical. – John Lawler Jun 20 '18 at 18:48
  • It's a free choice in integrated relatives like your example. They show no semantic difference and no syntactic difference other than what follows from "that" not being relative pronoun, but a subordinator. – BillJ Jun 20 '18 at 19:27
  • Broadly, it hardly matters but to anyone who cares, "that" defines and "which" explains.

    Prove this simply by comparing "that which" to "which that"…

    Is either of those aceptable? Then, why?

     – Robbie Goodwin Jun 22 '18 at 19:59

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