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How to prove that $e^{−7X}$ is a random variable, given that $X$ is a random variable.

Additionally, ¿can you provide a bibliography to learn more on this topic?. I also wanna know the proof that $ln(X)$ is a random variable.

Alvaro Morales
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    If this is an exercise, consider: What does it take for something to be a random variable (what properties does it imply for $X$)? ... (on the other hand if you're just trying to learn the concept in an intuitive way, I suggest starting with this answer: https://stats.stackexchange.com/questions/50/what-is-meant-by-a-random-variable/54894#54894 ) ... as for books, just about any decent book on probability and mathematical statistics should probably suffice, if it's close to the level you're working at – Glen_b May 17 '22 at 23:28

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If X is a random variable, then e^{-7X} is a transformation of that random variable, and is also just a random variable. It's as easy that, I think.

ingoingpigeon
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    It's easy, but this answer misses the point. Not every transformation of a random variable is a random variable. You have to appeal to the measurability of the function $x\to \exp(-7x).$ – whuber May 18 '22 at 13:56