For any r.v. and , the following are true:

  • for any constant .

This ties back to us “doubling” r.v. . Multiplying by two doesn’t change the probabilities, but the values that supports. This should intuitively also update when .

Derived properties

For any constant , we have for any constant . This makes sense because we’re saying a r.v. always.

If uses hours and we want to express as minutes, these are equivalent: . This makes intuitive sense, we’re simply switching units.

Combining these properties, we also have .