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Chapter 5: Q.5.7 (page 215)

The standard deviation of X, denoted SD(X), is given by

SD(X)=Var(X)

Find SD(aX+b) if X has variance σ2.

Short Answer

Expert verified

The value ofSD(aX+b)=|a|σ.

Step by step solution

01

Given Information

The standard deviation of X, denoted SD(X).

02

Explanation

To find SD(aX+b):

Using the definition of standard deviation and basic properties of Variance, we have that

SD(aX+b)=Var(aX+b)=a2Var(X)=|a|Var(X)=|a|σ

since we have that Var(X)=σ2⇒SD(X)=σ.

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