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:

Justified Warfare

Warfare that is deemed defensible by ethical or moral standards, often discussed within the context of just war theory.

Large Scale

Referring to activities, operations, or phenomena that are extensive in size, scope, or impact.

Great Purpose

A significant aim or goal that guides actions and gives meaning to one's life.

Unlawful Combatants

Individuals engaged in conflict without legal recognition or protection under international law, often denied prisoner of war status.