Theorem 5.4. Let X be a continuous r.v. with p.d.f. fx(x). Let y = g(x) be strictly monotonic (increasing or decreasing) function of x. Assume that g(x) is differentiable (and hence continuous) for all x. Then the p.d.f. h(.) of the r.v. Y is given by : dx hy(y) = fx(x)| (5-22) %3D ... where x is expressed in terms of y, and the range of Y is determined from the given range of the variable X, on using the transformation y = g(x).

Theorem 5.4. Let X be a continuous r.v. with p.d.f. fx(x). Let y = g(x) be strictly monotonic (increasing or decreasing) function of x. Assume that g(x) is differentiable (and hence continuous) for all x. Then the p.d.f. h(.) of the r.v. Y is given by : dx hy(y) = fx(x)| (5-22) %3D ... where x is expressed in terms of y, and the range of Y is determined from the given range of the variable X, on using the transformation y = g(x).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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