if X is random variable, is Y=2X+1 also random variable?

Question

I'm not very familiar with the random variable! I just know X is random variable, is Y here is also a random variable?How does X is related to Y? Can someone help me out, using the example to show me??thanks very much!!
I take an example, I Let X be the number of random numbers selected from{ 0,1,2,..9} independently until 0 is selected. what is probability mass function of Y=2X+1?
Please use this ex

Answer 1

Function of random variable is also random variable unless first random variable cancel itself in the function.
when x is random variable if it is related to Y by the function you have given. it has to random variable
Answer is YES

Answer 2

I'd say do your homework yourself. Your task is just a simple function and the answer to your question is "yes".