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Probability : What happens when you square a random variable?

Please solve for Problem #3.1.

3.1 What happens when you square a random variable?
Let X be a continuous random variable with p.d.f fX, and let Y=X^2
Show that:

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Squaring a random variable is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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