support of density function

Question

A random variable Y has density function f(y) = y/4 for 1<=y<3, and 0 elswhere.

The question states: Find the support of U=3Y -2, that is , find the range of real numbers u for which the density function of U is positive.

I am not sure what is the meaning of the term ‘support’ (I cannot find a definition in my text, but my understanding is that it refers to the domain or range of a function)

If this is correct, then my answer is 1<=U<7 (by substituting (U + 2)/3 into the given range of y.

But I get the density function of u to be (u +2)/36 for 1<=U<7, so the range of real numbers for which the density function of U is positive is u > -2.

Could anyone plse help clarify the term ‘support’ and whether the definition ‘the range of real numbers u for which the density function of U is positive’ is correct, and how do we obtain the support of Y.

Answer 1

The question states the meaning of "support":

Find the support of $U = 3Y - 2$; that is, find the range of real numbers $u$ for which the density function of $U$ is positive.

The boldface part is the explanation of the meaning of "support."

You have correctly determined that the support of $U$ is $1 \le U < 7$.