Let Z be a N(0, 1) random variable, and let F(x) be thecumulative distribution function for Z. Show that on S (∞, 0], F(x) is an increasing convex function, and on S [0, ∞), F(x) is an increasing concave function.

Let Z be a N(0, 1) random variable, and let F(x) be thecumulative distribution function for Z. Show that on S (∞, 0], F(x) is an increasing convex function, and on S [0, ∞), F(x) is an increasing concave function.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 32E

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Let Z be a N(0, 1) random variable, and let F(x) be the
cumulative distribution function for Z. Show that on S
(∞, 0], F(x) is an increasing convex function, and on S
[0, ∞), F(x) is an increasing concave function.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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