The Standard Deviation for a Random Variable with Probability Density $f$

question 50

Multiple Choice

The standard deviation for a random variable with probability density function $f$ and mean $\mu$ is defined $\sigma = \left[ \int _ { - \infty } ^ { \infty } ( x - \mu ) ^ { 2 } f ( x ) d x \right] ^ { 1 / 2 } .$ Find the standard deviation for an exponential density function with mean 10 .

• A) 10
• B) 2
• C) 5
• D) \(3.3\)
• E) \(2.5\)

---

Definitions:

Confederate South

The southern states of the United States that seceded from the Union in 1860-61, forming the Confederate States of America, leading to the American Civil War.

Punishable by Death

Certain crimes or legal offenses deemed so severe that they carry the death penalty as a potential form of punishment.

Glorieta Pass

A significant site of the American Civil War, located in New Mexico; it was the scene of a decisive battle in 1862.

Union Victory

The term refers to the triumph of the Northern states, the Union, over the Confederate states in the American Civil War, leading to the preservation of the United States and the abolition of slavery.