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

question 93

Short Answer

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 .

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Definitions:

Classified Balance Sheet

A balance sheet that organizes assets and liabilities into subcategories like current, long-term, property, plant, and equipment, to provide more detailed information.

Current Ratio

It's a financial ratio that calculates whether a corporation can cover its obligations that need to be paid within one year, by dividing the current assets by the current liabilities.

Plant Assets

Tangible assets that are used in the operations of a business and are not intended for resale, including buildings, machinery, and equipment.

Natural Business Year

The fiscal year that ends when a business's activities have reached the lowest point in its annual operating cycle, theoretically the most optimal time for financial reporting.