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

question 123

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) \(2.5\)

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Definitions:

Liquidations

The process of winding up a company's financial affairs by selling off assets to pay creditors and distribute any remaining assets to shareholders.

Calls in Advance

Funds received by a company from its shareholders before they are actually called for, typically for the issue of shares.

Voluntary Winding Up

The process initiated by a company's shareholders to voluntarily dissolve the company and liquidate its assets for distribution.

Special Resolution

A shareholder resolution that requires at least a 75% majority vote to pass, often related to significant corporate actions.