Let F be a continuous strictly increasing c d f with p d f f Let V have the uniform distribution on the interval a, b with 0 a b 1 Prove that the p d f of X F1(V) is f (x) (b a) for F1(a) x F1(b) (If a 0, let F1(a) If b 1, let F1(b) ) ...

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Let F be a continuous strictly increasing c.d.f. with p.d.f. f . Let V have the uniform

Question:

Let F be a continuous strictly increasing c.d.f. with p.d.f. f . Let V have the uniform on the interval [a, b] with 0 ≤ a < b ≤ 1. Prove that the p.d.f. of X = F−1(V) is f (x)/(b − a) for F−1(a) ≤ x ≤ F−1(b). (If a = 0, let F−1(a) = −∞. If b = 1, let F−1(b) = ∞.)
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...