Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { n }$

question 22

Essay

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { n }$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma ^ { 2 }$ . Then the random variable $( n - 1 ) S ^ { 2 } / \sigma ^ { 2 }$ has a __________ probability distribution with __________ degrees of freedom.

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Definitions:

Loan to Value Ratio

A financial term used by lenders to express the ratio of a loan to the value of an asset purchased.

Amortized

Relates to spreading payments over multiple periods to gradually eliminate a liability or loan, incorporating both principal and interest components.

Compounded Semiannually

The calculation of interest where the interest earned over a period is added to the principal, and the process is repeated twice a year.

Gross Debt Service Ratio

A financial ratio that compares an individual's monthly housing costs (including mortgage payments, property taxes, and utilities) to their gross monthly income, used by lenders to assess borrowing capacity.