40 Let f(x) be any pdf with mean μ and variance o2. Show how to create a location-scale family based on f(x) such that the standard pdf of the family, say f*(x), has mean 0 and variance 1. 41 A family of cdfs {F(x0), 0 0} is stochastically increasing in 0 if 0₁ > 02 ⇒ F(x|0₁) is stochastically greater than F(x|02). (See Exercise 1.49 for the definition of stochas- tically greater.)

A First Course in Probability (10th Edition)
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40 Let f(x) be any pdf with mean and variance o2. Show how to create a location-scale
family based on f(x) such that the standard pdf of the family, say f*(x), has mean 0
and variance 1.
41 A family of cdfs {F(x0), 0 } is stochastically increasing in 0 if 0₁ > 02 ⇒ F(x|0₁)
is stochastically greater than F(x|02). (See Exercise 1.49 for the definition of stochas-
tically greater.)
Transcribed Image Text:40 Let f(x) be any pdf with mean and variance o2. Show how to create a location-scale family based on f(x) such that the standard pdf of the family, say f*(x), has mean 0 and variance 1. 41 A family of cdfs {F(x0), 0 } is stochastically increasing in 0 if 0₁ > 02 ⇒ F(x|0₁) is stochastically greater than F(x|02). (See Exercise 1.49 for the definition of stochas- tically greater.)
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