3. Let X be a random variable with distribution function P(X ≤x} = { 0 x 1 if x ≤ 0, if 0 < x ≤ 1, if x > 1. Let F be a distribution function which is continuous and strictly increasing. Show that Y = F-¹(X) is a random variable having distribution function F. Is it necessary that F be continuous and/or strictly increasing?

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A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…