(Solution) - Consider an Exponential random variable X with parameter -(2025 Original AI-Free Solution)

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Consider an Exponential random variable X with parameter ? > 0.
Is it always true that, if a and b are positive constants, then Y = aX + b is an Exponential random variable too?
If your answer is "yes," then give a justification (e.g., give an argument in favor).
If your answer is "no," then give a very concrete counterexample (e.g., for at least one specific a and b of your choice, show that Y = aX + b is not Exponential).