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:

Par Value

The face value of a bond or the stock value stated in the corporate charter, which is typically a minimal amount not reflective of the market value.

Installment Note

A debt instrument that requires a series of payments over time, often including both interest and principal.

Annual End-Of-Year

A term typically referring to financial transactions or reports that are calculated, summarized, or finalized at the end of the fiscal year.

Journal Entries

Records of financial transactions in the accounting system, detailing the accounts affected and whether they are debits or credits.